Question

The weight of $\tfrac13$ of a large pizza together with $3\tfrac12$ cups of orange slices is the same as the weight of $\tfrac34$ of a large pizza together with $\tfrac12$ cup of orange slices. A cup of orange slices weighs $\tfrac14$ of a pound. What is the weight, in pounds, of a large pizza?

$1\tfrac45$

$2$

$2\tfrac25$

$3$

$3\tfrac35$

Solution:

Let the pizza weigh $P$ pounds. Then $3\tfrac12$ cups weigh $\tfrac72\cdot\tfrac14=\tfrac78$ and $\tfrac12$ cup weighs $\tfrac12\cdot\tfrac14=\tfrac18.$

The equation is $\tfrac13 P+\tfrac78=\tfrac34 P+\tfrac18.$

Subtracting gives $\tfrac78-\tfrac18=\left(\tfrac34-\tfrac13\right)P,$ so $\tfrac34=\tfrac{5}{12}P$ and $P=\dfrac{9}{5}=1\tfrac45.$

Thus, the correct answer is A.

2023 AMC 12A Problem 2

Solution:

Problem 2 in Other Years