Question

 PLS HELP NEED IN AN HOUR The school soccer teams went to the local smoothie shop to get smoothies after practice. Each large smoothie costs the same amount, and each small smoothie costs the same amount.

The girls soccer team paid $65 total for 10 large smoothies and 5 small smoothies
• The boys soccer team paid $77 total for 14 large smoothies and 3 small smoothies
Write the system of equations that would be used to find × the cost of a small smoothie and y the cost of a large smoothie?
What is the cost in dollars for each large smoothie? Show your work.

Answer 1

This is a system of linear equations problem. Let's denote:

x = cost of a small smoothie

y = cost of a large smoothie

Given the problem, we know:

10y + 5x = $65 (This is the cost for the girls' soccer team)

14y + 3x = $77 (This is the cost for the boys' soccer team)

This is our system of equations.

To find the cost of a large smoothie (y), we can use substitution or elimination. In this case, let's use elimination.

First, we can multiply the first equation by 3 and the second equation by 5 to make the coefficients of x the same in both equations:

30y + 15x = $195

70y + 15x = $385

Now, if we subtract the first equation from the second, the x terms will cancel out:

40y = $190

Dividing both sides by 40, we get:

y = $190 / 40 = $4.75

So, each large smoothie costs $4.75.