For large parties of children, a restaurant uses a formula to determine the number b of ice cream bars to buy if c children will attend. Ice cream bars are sold only in boxes of 24. If 14 boxes of bars were bought when 150 children attended, and if 16 boxes were bought when 175 attended, which of the following could be the formula used by the restaurant?
(A) b = c+25
(B) b = c+175
© b = 2c
(D) b = 2c+25
(E) b = 3c+10
I don’t understand this question, and the answer is D
Thanks.
Here, let c = 150. b is the number of ice cream bars bought, not the number of boxes bought (in this case 14). Since 14 boxes were sufficient to feed the children, we have that 1324 < b ≤1424, or 312 < b ≤ 336.
Therefore, when c = 150 children attended, the restaurant bought b bars where 312 < b ≤ 336. Plugging into the answer choices we see that either (B) or (D) works, as b equals 325 in either case.
Let c = 175, and using the same reasoning as above we get 360 < b ≤ 384. However only choice (D) satisfies the constraint, since the equation in (B) gives b = 350. So (D) is the answer.
Thank you so much!