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?
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.
