Question

Use a system of equations to solve this problem.

Julie needs 8 ounces of snack mix that is made up of seeds and dried fruit. The seeds cost $1.25 per ounce and the dried fruit costs $2.25 per ounce. The 8 ounce snack mix costs $2.00 per ounce.

Let x = the amount of seeds.

Let y = the amount of dried fruit.

How much of each snack should Julie purchase to satisfy the scenario?

6 ounces of seeds and 2 ounces of dried fruit


2 ounces of seeds and 6 ounces of dried fruit


5 ounces of seeds and 3 ounces of dried fruit


3 ounces of seeds and 5 ounces of dried fruit

Answer 1

The answer is 2 ounces of seeds and 6 ounces of dried fruit

x = the amount of seeds in ounces.
y = the amount of dried fruit in ounces.

Julie needs 8 ounces of snack mix that is made up of seeds and dried fruit:
x + y = 8

The seeds cost $1.25 per ounce: 1.25x
The dried fruit costs $2.25 per ounce: 2.25y
The 8 ounce snack mix costs $2.00 per ounce:
1.25x + 2.25y = 8 * 2.00
1.25x + 2.25y = 16.00

The system of equations is:
x + y = 8
1.25x + 2.25y = 16.00
________________
Divide the second equation by 0.25:
x + y = 8
1.25x/0.25 + 2.25y/0.25 = 16.00/0.25
________________
x + y = 8
5x + 9y = 64
______
Express the first equation in the terms of x:
x = 8 - y
5x + 9y = 64
______
Substitute x from the first equation into the second one:
5 * (8 - y) + 9y = 64
40 - 5y + 9y = 64
40 + 4y = 64
4y = 64 - 40
4y = 24
y = 24/4
y = 6 ounces of dried fruit

Since x = 8 - y and y = 6, then:
x = 8 - 6 = 2 ounces of seeds

So, Julia needs 2 ounces of seeds and 6 ounces of dried fruit.