Question

Solve by showing your work

A bakery is having a big event. They need to bake cookies and brownies. Bakery has 120 oz of dough available. Each cookie needs 2 oz of dough and each brownie needs 3 oz of dough.
Equation - 2c + 3(20) = 120
Inequality - 2(10) + 3b≤120

Answer 1

Write the dough constraint first:
2c + 3b ≤ 120 (c = number of cookies, b = number of brownies)

1) Equation given: 2c + 3(20) = 120
3·20 = 60, so 2c + 60 = 120
2c = 120 − 60 = 60
c = 60/2 = 30
So if they make 20 brownies, they can make 30 cookies.

2) Inequality given: 2(10) + 3b ≤ 120
2·10 = 20, so 20 + 3b ≤ 120
3b ≤ 120 − 20 = 100
b ≤ 100/3 ≈ 33.33
Since b must be a whole number, the bakery can make at most 33 brownies if they make 10 cookies.

(Also note the extremes: if no brownies, max cookies = 120/2 = 60; if no cookies, max brownies = 120/3 = 40.)