Keisha is catering a luncheon. She has $30 to spend on a mixture of Cheddar cheese and Swiss cheese. How many pounds of cheese can Keisha 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 with Step-by-step explanation:

I would like to answer Part 4 first.

Part 4: What linear equation in standard form can she use to model the situation?

The situation says:

A total of $30 can be spent on "x" number of pounds of Cheddar Cheese and "y" number of pounds of Swiss Cheese.

Mathematically:

$30 = A*x + B*y

Here "A" is the price of Cheddar cheese and "B" is the price of Swiss cheese.

Part 1: How many pounds of cheese can Keisha get if she buys only Cheddar cheese?

If she is going to buy only Cheddar cheese it means she will not buy Swiss which means "Y=0". This implies that:

$30 = A*x + B*0

$30 = A*x

x = $30 / A

I don't know the price of Cheddar Cheese, we can suppose it is $6 per pound.

So by putting values, we have:

x = $30 / $6 = 5 pounds

Part 2: Only Swiss cheese?

Just like part 1, here "X=0". This implies that:

$30 = A*0 + B*y

$30 = B*y

x = $30 / B

I don't know the price of Swiss Cheese, we can suppose it is $10 per pound.

So by putting values, we have:

x = $30 / $10 = 3 pounds

Part 3: A mixture of both cheeses?

There is number of answers to this question because the purchase of the type of cheese depends upon Keisha's priorities and desires.