First, make sure to label what x and y represent. In this problem, x represents the strawberry smoothies and y represents the protein shakes. The easiest way to solve this problem is by using the substitution method. The substitution method means that you're going to solve for one variable and plug that value in for the other. Let's do it!
If we take the first equation and solve for x, we get a new equation: x= 25.50-4y
We can take that equation and substitute 25.50 - 4y for x in the other equation: 3*(25.50 - 4y) + 2y = 24.00
Using the distributive property, we multiply 3 by 25.50 and 4y to get: 76.50 - 12y + 2y = 24.00
Since we have managed to write the equation so that we solve for y, which is the cost of a protein shake, once we do this, we will have our answer.
76.50 - 12y + 2y = 24.00 rewriting the equation
76.50 - 10y = 24.00 combine like terms (-12y +2 = -10y)
-76.50 -76.50 subtract 76.50 from both sides
-10y = -52.50 simplify
÷-10 ÷-10 divide both sides by -10
y = 5.25 simplify
We now see that protein shakes cost $5.25 each! We can check by solving for x with our original equation and plugging both values back in.
