A grocery bag has some apples and plums in it. There are 10 total pieces of fruit in the bag. The total weight of the apples and plums in the bag is 32 ounces. Each apple weighs 5 ounces, and each plum weighs 2 ounces.

Question

Take a look at the table. All of these combinations equal 10 total pieces of fruit. Which combination of apples and plums weighs 32 ounces? That’s the combination of fruit that is in the bag.
Number of
apples Number of
plums Total weight
in ounces
10 0 50
9 1 47
7 3 41
4 6 32
2 8 26
0 10 20
apples and
plums weigh 32 ounces.

Answer 1

To find the combination of apples and plums that weighs 32 ounces, let's summarize the conditions based on the information provided.

Let:

• \( a \) = number of apples
• \( p \) = number of plums

We have the following equations:

1. \( a + p = 10 \) (total pieces of fruit)
2. \( 5a + 2p = 32 \) (total weight in ounces)

From the first equation, we can express \( p \) in terms of \( a \): \[ p = 10 - a \]

Substituting this expression for \( p \) into the second equation: \[ 5a + 2(10 - a) = 32 \] \[ 5a + 20 - 2a = 32 \] \[ 3a + 20 = 32 \] \[ 3a = 12 \] \[ a = 4 \]

Now, substituting back to find \( p \): \[ p = 10 - 4 = 6 \]

So there are 4 apples and 6 plums in the bag.

To confirm, we can check the total weight:

• Weight of apples: \( 4 \times 5 = 20 \) ounces
• Weight of plums: \( 6 \times 2 = 12 \) ounces
• Total weight: \( 20 + 12 = 32 \) ounces

Thus, the combination of 4 apples and 6 plums weighs 32 ounces.