Question

Chloe purchased some dried mango and dried kiwi to make some trail mix. The dried mango cost ​$2.11 per pound and the dried kiwi cost ​$5.07 per pound. If she spent ​$40.34 for 10 pounds of dried​ fruit, how many pounds of each fruit did she​ have?

Answer 1

Number of pounds of dried mangoes Chloe bought = 3.5

Number of pounds of dried kiwi Chloe bought bough = 6.5

Explanation:

Total number of pounds of dried fruit purchased = 10

Let number of pounds of dried mango purchased =
`x`

Let number of pounds of dried kiwi purchased be =
`y`

Total weight of dried fruits purchased =
`x+y`

So, we have a sum equation as:

`x+y=10`

Total cost of dried fruits = $40.34

Cost of a pound of dried mango = $2.11

Cost of
`x` pounds of dried mango in dollars can be given as =
`2.11x`

Cost of a dried kiwi = $5.07

Cost of
`y` pounds of dried kiwi in dollars can be given as =
`5.07y`

Total cost of dried fruits in dollars =
`2.11x+5.07y`

So, we have a cost equation as:

`2.11x+5.07y=40.34`

The system of equations is :

A)
`x+y=10`

B)
`2.11x+5.07y=40.34`

Solving by substitution.

Rearranging equation A, to solve for
`y` in terms of
`x`

Subtracting both sides by
`x`

`x+y-x=10-x`

`y=10-x`

Substituting value of
`y` we got from A into equation B.

`2.11x+5.07(10-x)=40.34`

Using distribution.

`2.11x+50.7-5.07x=40.34`

Simplifying.

`-2.96x+50.7=40.34`

Subtracting both sides by 50.7.

`-2.96x+50.7-50.7=40.34-50.7`

`-2.96x=-10.36`

Dividing both sides by -2.96.

`(-2.96x)/(-2.96)=(-10.36)/(-2.96)`

∴
`x=3.5`

We can plugin
`x=3.5` in the rearranged equation A to get value of
`y`

`y=10-3.5`

∴
`y=6.5`

So, number of pounds of dried mangoes Chloe bought = 3.5

Number of pounds of dried kiwi Chloe bought bough = 6.5