Jeff and his friends went to a juice bar. Jeff ordered 3 smoothies and 5 fruit punches for a total of
28. His friend ordered 4 smoothies and 2 fruit punches for a total of 22. Another friend ordered 2 smoothies and 3 fruit punches for a total of $16. The price of a smoothie is the same, and the price of a fruit punch is also the same. What is the cost of each smoothie and each fruit punch?
Let's assume the price of a smoothie is "s" and the price of a fruit punch is "f."
We can create the following equations based on the given information:
3s + 5f = 28 ----(1)
4s + 2f = 22 ----(2)
2s + 3f = 16 ----(3)
We'll solve this system of equations using substitution method:
From equation (2), we can write 4s = 22 - 2f, or s = (22 - 2f)/4 = (11 - f)/2 ----(4)
Substituting equation (4) in equation (3), we get:
2((11 - f)/2) + 3f = 16
11 - f + 3f = 16
2f = 16 - 11
2f = 5
f = 5/2
f = 2.5
Substituting the value of f in equation (1), we get:
3s + 5(2.5) = 28
3s + 12.5 = 28
3s = 28 - 12.5
3s = 15.5
s = 15.5/3
s = 5.16666
Rounded to two decimal places, the cost of each smoothie is $5.17 and the cost of each fruit punch is $2.50.