Question

At the store, bananas cost $0.50 per pound and apples cost $1.25 per pound. Diego purchased bananas and apples and spent $2.75. a. Write a linear equation in standard form for Diego's purchase. b. Use you equation to determine how many pounds of apples he bought if he purchase 3.5 pounds of bananas.

Answer 1

Part a:

Linear equation: 1.25x + 0.50y = 2.75

Part b: 0.8 pounds of apples

Explanation:

Part a.

Let x represent the number of pounds of apples that Diego bought and let y represent the number of pounds of bananas that he bought.

Since, bananas cost $0.50 per pound and apples cost

$1.25 per pound.

Diego purchased bananas and apples and spent $2.75.

The linear equation in standard form for Diego's purchase will be:

`\boxed{\boxed{\sf 1.25x + 0.50y = 2.75}}`

Part b.

Since Diego purchased 3.5 pounds of bananas, we can substitute y = 3.5 into the equation to find the number of pounds of apples he bought:

0.5(3.5) + 1.25x = 2.75

1.75 + 1.25x = 2.75

Subtract 1.75 on both sides:

1.75 + 1.25x - 1.75 = 2.75 - 1.75

1.25x = 1

Divide both sides by 1.25.

`\sf (1.25x)/(1.25)=(1)/(1.25)`

x = 0.8

Therefore, Diego bought 0.8 pounds of apples.