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