Question

Fatima is buying cheese for a party. She has $45 to spend on a mixture of Cheddar cheese and Swiss cheese. Cheddar cheese costs $5 per pound and Swiss Cheese costs $7 per pound. How many pounds of cheese can Fatima get if she buys only Cheddar cheese? Only Swiss cheese? A mixture of both cheeses? What linear equation in standard form can she use to model the situation?

Answer 1

Given:

a.) Fatima has $45 to spend on a mixture of Cheddar cheese and Swiss cheese.

b.) Cheddar cheese costs $5 per pound.

c.) Swiss Cheese costs $7 per pound.

1.) How many pounds of cheese can Fatima get if she buys only Cheddar cheese?

We divide the $45 that Fatima has by the price of the Cheddar.

$\text{Pounds of Cheddar = }\frac{\text{ \ 45}}{Price\text{ of Cheddar per pound}}$$\text{Pounds of Cheddar = }\frac{\text{ \ 45}}{\text{ \ 5}}$$\text{Pounds of Cheddar = }9$

Therefore, Fatima can buy 9 pounds of Cheddar cheese for $45.

2.) How many pounds of cheese can Fatima get if she buys only Swiss cheese?

We divide the $45 that Fatima has by the price of the Swiss cheese.

$\text{Pounds of Swiss cheese = }\frac{\text{ \ 45}}{Price\text{ of Swiss cheese per pound}}$$\text{Pounds of Swiss cheese = }\frac{\text{ \ 45}}{\text{ \ 7}}$$\text{Pounds of Swiss cheese = }6.428571\text{ }\approx\text{ 6.43}$

Therefore, Fatima can buy 6.43 pounds of Swiss cheese for $45.

3.) A mixture of both kinds of cheese? What linear equation in standard form can she use to model the situation?

$\text{ 5x + 7y = 45}$

Where,

x = number of Cheddar cheese

y = number of Swiss cheese