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| Ummmmm! |
2-for-1 Lunch
Trey and Andrew had just completed a particularly strenuous algebra class. They needed a break. Andrew was exhausted. "Boy, I'm glad to be out of there. I'll never use this stuff anyway." Trey agreed. "Yeah, let's go to Joe's Deli for lunch. I don't want to think about math for a while."
"May I take your order?" asked the Joe's Deli waiter. Trey was pretty hungry. "I'd like a double cheeseburger with fries and a triple chocolate fudge sundae." That sounded good to Andrew. "Make that two," he added. Trey was feeling pretty smug. "That two-for-one coupon makes this lunch even better. All of this and we're saving 50%."
"Yep, a no brainer," agreed Andrew. "We don't need math class to figure this one out."
Your challenge: Assume that the price of each meal is $P. The value of one of the meals is deducted from the total bill. A sales tax of 8 1/4% will be paid on one of the meals, but the 15% tip will be paid on both meals.
Were the boys correct in their assertion that the percentage of savings is 50%? If yes, why? If not, what is the percentage of savings (rounded to the nearest whole percent)?
Please solve the problem in the general case as stated using $P, and not a specific number for P.
Bonus: Suppose the prices of two meals are $P and $A, with P > A. The two-for-one coupon states that you drop the meal of lower value. Assume the 8 1/4% tax is paid on the more expensive meal, and the 15% tip is paid on both meals.
- Find an expression for the percentage of savings in terms of A and P.
- Use this expression to show that the maximum savings occur when A = P.
A.L.
ReplyDeleteChallenge: They boys were not correct in their assumption that they will save 50%. Where they went wrong in the assumption was on the tip. Since they’re paying a 30% tip for the overall cost, you have to divide that by the $P and therefore they are only going to save 33% on the overall cost. I got this by figuring out what 1/3 of 50 is since there are three parts that make up 50% of the bill. I got 16.6666667, so I rounded up to 17, then subtracted 17 from 50 and got 33. So that then became my percentage of savings.
HW
ReplyDeleteThe two boys were not correct that the saving percentage is 50%, they save 44%. I figured that out by replacing P in my equation with 5, and then working it out, which gave me 6.974375. I then worked the equation 5(1.0825)(1.15) + 5(1.0825)(1.15) to figure out what the two meals would cost without the two for one deal, which is 12.44875. I then divided 6.984375 by 12.44875 and got 0.5602… and since .56 is 56%, and 100% - 56% = 44%, the boys saved a total of 44%.
This is how I got my equation: The two boys are getting two for one, and each meal costs $P. A tax of 8 1/4% is paid on one of the meals, so to find the cost of the meal with the tax you need to do P(1.0825) and figure out what that is. A 15% tip will be paid on both meals, and since one of the meals got a tax, you would have to multiply the meal cost including the tax by 1.15, so the equation to find the total cost of that meal would be P(1.0825)(1.15). The other meal also needs a tip, and since it didn’t have a tax the equation to find the meal cost would be P(1.15). Then, to find the total cost of the two meals with the two for one coupon it would be P(1.0825)(1.15) + (P(1.15) – P).
LG
ReplyDeleteThe whole check would not be half off because Treys burger, ice cream, and fires are paid plus the tax of 8 1/4 % and the tip 15% at the end of the check and Andrew’s is free with no tax.
AR
ReplyDeleteThe boys are not getting exactly 50% off. In fact, they are getting less than 50% off. The equation for the two-in-one is [P1.0825 (1.15)] + P1.15 - P. The actual percentage that they are saving is 44%. The price of the two-in-one is 4.19. The combined price if they bought their meals separately is 7.48. If 4.19 is divided by 7.48 is 56%. The reason that they aren’t saving 56% is because that is how many times 7.48 goes into 4.19. The 44% comes from the rest of that 56% because the 44% will be the difference from 4.19 to 7.48. Now, if the two-in-one did not include the tip for the meal that doesn’t have a tax which is $.45, it would be 50%. And the easiest way to tell that it’s not 50% is that 4.19(the two-in-one price) is higher than 3.74(the price of each meal by itself).
TM
ReplyDeleteThe boys are getting just under 50% savings for their meal. The equation to get the total for the combo meals is p(1.0825)(1.15)+(p)(1.15)-p. Since the tip is applied to both there is no way they could get exactly 50% off because you are paying something for both. If they were paying the same amount of extras for both beyond the price they would be getting exactly getting 50% off. The exact percent they are getting is 44%. I found this by using by plugging number is for P and then dividing the final cost of both by the cost of just the first one, in essence the change of cost between the one they are paying sales tax on and the one they are not.
AR
ReplyDeleteThe boys are not getting exactly 50% off. In fact, they are getting less than 50% off. The equation for the two-in-one is [P1.0825 (1.15)] + P1.15 - P. The actual percentage that they are saving is 44%. If each meal is 3$, the price of the two-in-one is 4.19. The combined price if they bought their meals separately is 7.48. If 4.19 is divided by 7.48 it is 56%. The reason that they aren’t saving 56% is because that is how many times 7.48 goes into 4.19. The 44% comes from the rest of that 56% because the 44% will be the difference from 4.19 to 7.48. Now, if the two-in-one did not include the tip for the meal that doesn’t have a tax which is $.45, it would be 50%. And the easiest way to tell that it’s not 50% is that 4.19(the two-in-one price) is higher than 3.74(the price of each meal by itself).
A.L.
ReplyDeleteChallenge: They boys were not correct in their assumption that they will save 50%. Where they went wrong in the assumption was on the tip. Since they’re paying a 30% tip for the overall cost, you have to divide that by the $P and therefore they are only going to save 33% on the overall cost. I got this by figuring out what 1/3 of 50 is since there are three parts that make up 50% of the bill. I got 16.6666667, so I rounded up to 17, then subtracted 17 from 50 and got 33. So that then became my percentage of savings.
E.E.W.
ReplyDeleteTrey and Andrew are not right about that the percentage is 50%. They do only have to pay half of the price of the burger, and 50% is half, but they also have to consider the tax and tip percentage. I added the tip percentage with the tax percentage, and it is 23% rounded to the nearest whole number. Since they have to pay that 23% of the bill, they save 27%. (50-23=27). Then, you have to add the other 50%, and 100-23=73. They pay 73% of the bill.
LG
ReplyDeleteThe whole check would not be half off because Trey’s burger, ice cream, and fires are paid are free and so is Andrew's but Trey has to add the 8 ¼ % tax plus the 15% tip thus making it not half off.
BT
ReplyDeleteTrey and Andrew are not correct when they say that they are saving 50%. This is because even though they get 2 burgers for the price of 1, they still have to pay the 15% tip, and the 8 ¼ % tax. So, they would have to pay 23%. I figured this out by adding 15 (tip) and 8 ¼ (tax), which got me 23%. To figure out how much they saved, you would have to subtract 23 from 50, which is 27. Then, you would have to add the other 50% to 27%, which would mean that they paid 77% of their bill.
SK
ReplyDeleteC=Total Cost
P=Cost of one meal
The assumption that the savings are 50 percent is incorrect. When two meals are purchased using the coupon, the cost follows the equation C= 1.0825p + (.15p)2. If a single meal was purchased without the coupon, the cost follows the equation C=1.0825p + (.15p). Assuming the cost of the meal is one dollar, when you replace p with one dollar in each equation C= 1.38 for the equation for two people, and C=1.23 for only one person. If two people bought a meal without a coupon, C=2.46. 1.38 is not half of 2.46. The actual percentage is 50.2%
1. Trey and Andrew are not correct that they will save 50%. They pay 50% for the price of the meal, but they would need to consider tip and tax adding to the total. Using the equation $P x .0825 + ($P x .30), the percentage would be 0.66
ReplyDeleteM.J.S
ReplyDeleteThey think: 50%
I think he is wrong. With the tax and the and the tip there is no way that there only paying 50%. I’m going to say that the burgers are $10 each. The shakes are $4 each. The sundaes are $3 each.
I you add that all up you have $17 all together. Then you do the sales tax. You would multiply $17 by 2 to get $34. Then you multiply $17 by .0825 to get the tax of $1.40.
To get the tip you multiply $34 dollars by .15 to get $5.10.
The total amount would end up at $ 23.50
WO
ReplyDeleteC= Total Cost
P= Cost of One Meal
C=1.0825p+(0.15p)2
The two boys are incorrect in thinking that they are saving 50% on the meal. The cost follows the equation C=1.0825+(0.15p)2 when the two meals are bought. If it was a single meal, the equation would be C=1.0825+(0.15). When you replace the variable p with 1 dollar, the cost of the meal, than the equation for two people is C=1.38 and for a single person it is C=1.23. If there is no coupon used in purchasing the meal for two people, the equation is C=2.46. 1.38 is not half of 2.46 so the percentage is 50.2%.
RT
ReplyDeleteP=Cost of one meal
C=Total cost
C=1.0825p+ (0.15p) 2
Trey and Andrew’s assumption is incorrect in thinking that they are saving 50% on the meal. The cost follows the equation of C=1.0825p+(0.15p)2 when the two meals are being bought. If Trey and Andrew shared a single meal the equation would be 1.0825p+ (0.15p).When you replace the p with 1 dollar than the equation for the two people would be C=1.38 and for a single person the equation would be C=1.23. If there was no coupon used into buy the meals the equation for two people would be C=2.46. 1.38 is not half of 2.46 so the percentage is 50.2%.
AM
ReplyDeleteThis is what I did to get my equation. Trey and Andrew are getting two for one deal, and the cost is $P for one of their meals. The tax is 8 1/4% for one of the meals. To figure this problem out you need to multiply P(1.0825) and figure out what that is. The tip would be 15% for Trey’s and Andrew’s meals. One of the meals got tax and both of the meals had a tip of $1.15. Then add the tip to your answer of P(1.0825).
No they weren’t correct in their assertion because the meals aren’t the same and so that means that the savings can’t be 50%. The coupon only eliminates the lower priced meal. Even though they ordered the same thing, the thing that changes the price is the tax. It can’t be the tip because they both got the tip on the meal.
E.R.
ReplyDeleteTrey and Andrew didn’t save 50% on their meal. With the coupon, they would only have to pay $20 if the original cost of the meal was $40. They thought this, but didn’t account for the sales tax which was 8 ¼ %. Then they also had to pay they 15% tip for both meals. They would end up paying $21.65 for the meals and with the tip it would be $24.90. They would save $15.10 or 37.75%.
MF
ReplyDeleteTrey and Andrew did not get the 50% savings on their meal. Say the price of both meals is $20 each; they would have had to pay $40. But with the coupon they only have to pay $20. This is only what Andrew and Trey thought. There is still sales tax that they need to pay on one meal, which is 8 ¼ %.They also have to pay the 15% tip on both meals. Andrew and Trey did not think out the whole problem correctly. The cost of the meal would be $24.90. The savings of a meal that would cost $40 originally is $15.10. This would be 15.5% as a percent.
A.W.
ReplyDeleteChallenge: If the $P is 20 dollars and if Trey and Andrew used their two-for-one coupon,
the total of the meals would be 10. Then the sales tax for one meal would be .82 cents or 10.82 dollars. The tip for both meals would be 30 cents. So the total of the meal is $11.12. Thus Trey and Andrew’s assumption was wrong. If the total of their food was 10, then they would save 50% without the sales tax and the tip. But with the tip and sales tax they saved less than 50%. They actually saved 48.88%.
AWM
ReplyDeleteThe boys were wrong. The boys were wrong because they forgot to add the tax and tip. The boys would be saving 18%. They would be saving 18% because if the meals cost $10 each the tax is 8 1/4 % for only one meal and the tip is 15% for both meals. The expression would be Y= P15 divided by 8 1/4.
C.S
ReplyDeleteSince the total that the boys paid overall without the tip is $8.66, and the total with the tip is $11.06, they were wrong when they said that they would save 50%, because they did not include the tax for the meal, and the tip. Instead of saving 50%, they only save 34% with the coupon, because the tax rate for one meal is $0.66. The overall total that is coming out of their pockets is $11.06.
BILL:
FRIES:$1.00
DOUBLE CHEESE-BURGER:$4
TRIPPLE CHOCOLATE FUDGE SUNDAE: $3
TAX: $0.66
TOTAL:$8.64 EACH
$P=$8.00 EQUATION: $P x .0825 + ($P x .30)
$.66 is tax for 1 meal. $2.40 is the tip for both meals
MF
ReplyDeleteTrey and Andrew did not get the 50% savings on their meal. Say the price of both meals is $20 each; they would have had to pay $40. But with the coupon they only have to pay $20. This is only what Andrew and Trey thought. There is still sales tax that they need to pay on one meal, which is 8 ¼ %.They also have to pay the 15% tip on both meals. Andrew and Trey did not think out the whole problem correctly. The cost of the meal would be $28.15. The savings of a meal that would cost $40 originally is $11.85. This as a percent is 1185%.
M.M
ReplyDeleteOctober 15, 2010 blog done on October 29, 2010
Challenge: sales tax 8.25% tip: 3/20 P=$5 One meal with sales tax is $5.20 tip: 0.78$ 5.20+.78=5.98
Second meal without sales tax $5.00 tip:0.75$ 5.00+75=5.75
5.98+5.75=11.73
11.73-5.00=5.75
The boys were not correct when they thought their meals were 50% off. They forgot sales tax and tip. First, let’s say the meal is 5.00, you figure out the sales tax of ONE meal not on both which would be $.20 for one meal with sales tax, the other meal would still be $5.00 because we did not add sale tax on the second meal. Then, for both meals, you multiply 0.15 by $5.20 and $5.00. For $5.20 it would = 0.78 tip. For 5.00 your tip would be 0.75. Then you add your tip plus your cost of meal. For the meal with sales tax it would be $5.98, and for the meal without sales tax it would be $5.75. You add $5.75 and $5.78 together to get 11.73. You subtract $5.00 from $11.73 because $5.00 is the cost of the meal. That would equal $5.73. The boys are not correct because the meal is not exactly 50% off.
E.A.W.
ReplyDelete10/15/10
If Trey and Andrew used their two for one coupon the total price would be $10 instead of $20 and they would have saved 50% if there was no sales tax or tip (This is if the double cheeseburger was $5, the fries were $2, and the triple chocolate fudge sundae was $3.) but, there is going to be a sales tax for one meal and tip for both so their actual total would be $16.82 because the 8.25% sales tax for one ten dollar meal is 82 cents and the 15% tip for two ten dollar meals (a 30% tip for one twenty dollar meal) is $6. You add the sales tax and the tip to the $10 to get $16.82 which is not half or 50% of $20 dollars, which would be the total without a coupon, sales tax, or a tip. So, the percent would be 6.29% savings. (20-10=10 or 50% 20-16.82=3.18 20/3.18=6.29 or 6.29% of 20)
E.R.
ReplyDeleteTrey and Andrew didn’t save 50% on their meal. With the coupon, they would only have to pay $20 if the original cost of the meal was $40. They thought this, but didn’t account for the sales tax which was 8 ¼ %. Then they also had to pay they 15% tip for both meals. They would end up paying $21.65 for the meals and with the tip it would be $28.15. They would save $11.85. As a percent it would be 29.63%.
Arianna Williams
ReplyDeleteOctober 15 blog done on oct. 29
Challenge: first take the sales tax 8¼ % and multiply it by the original price of one of the
Ps. Then take the tip 15% and multiply it by both of the Ps. When you get the
Tax and tip add the tax to on P and add the tip to both Ps. You should end up
With numbers 5.98 and 5.75
Add the two numbers together and should get 11.73 duduct the original
Price of 5.00 from the 11.73 because of the two for one coupon, you now
Should have 5.73
Without the tax and the tip the total price would have been 10.00 with the
Coupon it would have been 5.00 but instead it is 5.73 so no the boys
do not save 50% the actually end up spending more money with the tax
and the tip. If there was no tax and tip than yes they would have saved
money.