Question

Lupe and her friends spent $20 on snack mix and water. They bought x bags of snack mix for $2.50 each and y bottles of water for $1.25 each. If Lupe and her friends bought a total of 11 items, how many bags of snack mix and bottles of water did they buy?

bags of snack mix: ?
bottles of water: ?

Answer 1

7.5 bags of snack mix, 3.5 bottles of water.

Explanation:

This can be found by looking at a system of equations. Setting up our system, we know that they bought 11 items, and that there was a total of $20. Our system would be this:

`x+y=11\\2.5x+1.25y=20`

We can then solve for a variable in any equation. Let's solve for x in the second equation.

`2.5x+1.25y=20\\2.5x=20-1.25y\\x=8-0.5\\x=7.5`

Now, we substitute into the other equation.

`x+y=11\\7.5+y=11\\y=11-7.5\\y=3.5`

We now know both amounts; they bought 7.5 bags of snack mix and 3.5 bottles of water.