2023 AMC 12A Problem 2

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

Let the pizza weigh

P

pounds; each cup of orange slices weighs

\tfrac14

Set the two weights equal and gather the

P

terms on one side

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.

Problem 2 in other years