Question

Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes $2.48 per pound. The cost of the fruit, before tax is $13.76. How many pounds of each fruit is she buying?

Answer 1

Hence She buys 4.5 pounds of apples and 2.5 pounds of grapes.

Explanation:

Cost of 1 pound of apple = $1.68

Cost of x pounds of apple = 1.68 x

She buys 2 fewer pounds of grapes i.e. (x-2) pounds.

Cost of 1 pound of grapes = $2.48

Cost of (x-2) pound of grapes = 2.48 (x-2)

The cost of the fruit, before tax is $13.76.

So,
`1.68 x+2.48 (x-2)=13.76`

`1.68 x+2.48x-4.96=13.76`

`4.16x-4.96=13.76`

`4.16x=13.76+4.96`

`4.16x=18.72`

`x=(18.72)/(4.16)`

`x=4.5`

She buys 4.5 pounds of apples.

She buys grapes = (x-2)=(4.5-2)=2.5 pounds

Hence She buys 4.5 pounds of apples and 2.5 pounds of grapes.

Answer 2

The number of pounds of apples is 4.5 and the number of pounds of grapes is 2.5

Explanation:

Let

x ------> the number of pounds of apples

(x-2) -----> the number of pounds of grapes

we know that

`1.68x+2.48(x-2)=13.76`

Solve for x

`1.68x+2.48x-4.96=13.76`

`1.68x+2.48x=4.96+13.76`

`4.16x=18.72`

`x=4.5\ pounds`

so

`x-2=4.5-2=2.5\ pounds`

therefore

The number of pounds of apples is 4.5 and the number of pounds of grapes is 2.5