on Tuesday Hayley only has 15 cups of flours and 9 eggs but she has more than enough butter and sugar which system of linear inequalities can Hayley use to model this situation when b represent the number of loves of banana and z represent the number of loves of zucchini bread
3b+2z is less than or equal to 15
b+2z is less than or equal to 9
thank u so much
Well, if Hayley wants to make banana bread and zucchini bread, we can set up the following system of inequalities:
1. For the cups of flour:
2b + 3z ≤ 15
This is because banana bread usually requires 2 cups of flour and zucchini bread requires 3 cups of flour. Hayley has a total of 15 cups of flour available.
2. For the number of eggs:
b + 2z ≤ 9
Since banana bread requires 1 egg and zucchini bread requires 2 eggs, Hayley has a total of 9 eggs available.
These inequalities ensure that Hayley doesn't use more flour or eggs than she has. Now, let's hope she has everything else she needs to bake her delicious bread!
To model the situation where Hayley has a limited amount of flour and eggs but an abundant supply of butter and sugar, we can set up a system of linear inequalities.
Let's denote the number of loaves of banana bread as 'b' and the number of loaves of zucchini bread as 'z'.
The constraints for the amount of flour and eggs can be represented as:
1. The amount of flour needed for each loaf of banana bread is 2 cups, so the total amount of flour used for 'b' loaves of banana bread is 2b.
Therefore, the constraint for flour is: 2b ≤ 15
2. The amount of flour needed for each loaf of zucchini bread is 3 cups, so the total amount of flour used for 'z' loaves of zucchini bread is 3z.
Therefore, the constraint for flour is: 3z ≤ 15
3. The number of eggs needed for each loaf of banana bread is 2 eggs, so the total number of eggs used for 'b' loaves of banana bread is 2b.
Therefore, the constraint for eggs is: 2b ≤ 9
4. The number of eggs needed for each loaf of zucchini bread is 1 egg, so the total number of eggs used for 'z' loaves of zucchini bread is z.
Therefore, the constraint for eggs is: z ≤ 9
Since we are only focusing on the constraints for flour and eggs (assuming butter and sugar are abundant), the system of linear inequalities can be written as:
2b ≤ 15
3z ≤ 15
2b ≤ 9
z ≤ 9
This system of linear inequalities models the situation where Hayley has limited amounts of flour and eggs but enough butter and sugar to make banana and zucchini bread.