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

Answer:

Number of pounds of dried mangoes Chloe bought = 3.5

Number of pounds of dried kiwi Chloe bought bough = 6.5

Step-by-step 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.

$\frac{-2.96x}{-2.96}=\frac{-10.36}{-2.96}$

∴ $x=3.5$

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