The total price of a shirt and a cap is $10. If the price of the shirt was doubled and the price of the cap was four times its original price, the total price of a shirt and a cap would be $26. The following system of equations models this scenario:
x + y = 10
2x + 4y = 26
What is the price of each shirt and cap?
We can use the first equation x + y = 10 to solve for one variable in terms of the other. For example, solving for y, we get:
y = 10 - x
We can substitute this expression for y into the second equation 2x + 4y = 26 and simplify:
2x + 4(10 - x) = 26
2x + 40 - 4x = 26
-2x = -14
x = 7
So the price of the shirt is $7. We can use either of the previous equations to solve for y:
y = 10 - x = 10 - 7 = 3
So the price of the cap is $3.