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`

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`