Question

The weight of $\frac{1}{3}$ of a large pizza together with $3\frac{1}{2}$ cups of orange slices is the same as the weight of $\frac{3}{4}$ of a large pizza together with $\frac{1}{2}$ cup of orange slices. A cup of orange slices weighs $\frac{1}{4}$ of a pound. What is the weight, in pounds, of a large pizza?

$1\frac{4}{5}$

$2$

$2\frac{2}{5}$

$3$

$3\frac{3}{5}$

Solution:

Let $p$ be the pizza's weight. A cup of orange slices is $\frac14$ pound, so the two sides balance as $\frac13 p + \frac72 \cdot \frac14 = \frac34 p + \frac12 \cdot \frac14,$ that is $\frac13 p + \frac78 = \frac34 p + \frac18.$ Collect the pizza terms: $\frac68 = \left(\frac34 - \frac13\right)p = \frac{5}{12}p.$ So $p = \frac34 \cdot \frac{12}{5} = \frac95 = 1\frac45.$ Therefore, the answer is A.

2023 AMC 10A Problem 2

Solution:

Problem 2 in Other Years