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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?

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MrRoyal

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:

[tex]2z + b \le 9[/tex]

[tex]2z + 3b \le 15[/tex]

Step-by-step explanation:

Given

[tex]Flour = 15[/tex]

[tex]Egg =9[/tex]

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

So, we have:

Zucchini Bread

[tex]Egg = 2[/tex]

[tex]Flour = 2[/tex]  

Banana Bread

[tex]Egg = 1[/tex]

[tex]Flour = 3[/tex]

For the eggs

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

[tex]Egg = 2[/tex] (z) : [tex]Egg = 1[/tex] (b)

This gives:

[tex]2z + 1b[/tex]

The total number of eggs cannot exceed 9.

So, the inequality is:

[tex]2z + 1b \le 9[/tex]

[tex]2z + b \le 9[/tex]

For the flours

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

[tex]Flour = 2[/tex] (z) :    [tex]Flour = 3[/tex] (b)

This gives:

[tex]2z + 3b[/tex]

The total cups of flours cannot exceed 15.

So, the inequality is:

[tex]2z + 3b \le 15[/tex]

Hence:

The system of inequalities is:

[tex]2z + b \le 9[/tex]

[tex]2z + 3b \le 15[/tex]

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