Question

On Tuesday, Hayley only has 15 cups of flour and 9 eggs, but she has more than enough butter and sugar. Which system of linear inequalities can Hayley use to model this situation, where b represents the number of loaves of banana bread and z represents the number of loaves of zucchini bread?

Answer 1

Missing part of the question

Hayley bakes zucchini bread and banana bread. Some ingredients Hayley uses for each type of  bread are shown in the tables

Zucchini Bread

2 eggs        2 cups of flour       1.5 cups of sugar        0.5 stick of butter

Banana Bread

1 egg          3 cups of flour        2 cups of sugar          0.25 stick of butter

Answer:

$2z + b \le 9$

$2z + 3b \le 15$

Step-by-step explanation:

Given

$Flour = 15$

$Egg =9$

Since there are enough of other ingredients, we will only consider the amount of eggs and cups of flour.

So, we have:

Zucchini Bread

$Egg = 2$

$Flour = 2$  

Banana Bread

$Egg = 1$

$Flour = 3$

For the eggs

The ratio of eggs to use in the Zucchini bread to Banana bread is:

$Egg = 2$ (z) : $Egg = 1$ (b)

This gives:

$2z + 1b$

The total number of eggs cannot exceed 9.

So, the inequality is:

$2z + 1b \le 9$

$2z + b \le 9$

For the flours

The ratio of flours to use in the Zucchini bread to Banana bread is:

$Flour = 2$ (z) :    $Flour = 3$ (b)

This gives:

$2z + 3b$

The total cups of flours cannot exceed 15.

So, the inequality is:

$2z + 3b \le 15$

Hence:

The system of inequalities is:

$2z + b \le 9$

$2z + 3b \le 15$