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

Write an equation to represent combinations of apples and plums that equal a total weight 32 oz. Let a represent the number of apples and p represent the number of plums. Remember, each apple weighs 5 ounces, and each plum weighs 2 ounces.

Answer 1

To create equations to represent the given problem, we need to define the variables and set up the equations based on the information provided.

Let:

• \(a\) be the number of apples,
• \(p\) be the number of plums.

From the information in the problem, we have the following two equations:

1. The total number of fruits (apples and plums) in the bag is 10: \[ a + p = 10 \]

2. The total weight of the apples and plums is 32 ounces. Since each apple weighs 5 ounces and each plum weighs 2 ounces, the weight equation can be expressed as: \[ 5a + 2p = 32 \]

Thus, the two equations that represent the combinations of apples and plums in the bag are:

1. \(a + p = 10\)
2. \(5a + 2p = 32\)