Question

“John is buying carpet for his house. He pays $1.30 per square foot for the first 1000 square feet. He pays $1.00 peradditional square foot after 1000 square feet.Part A: Write an equation for the total price when John buys less than 1000 square feet of carpet. Let c representthe amount of carpet needed in square feet, and p represent the total price in dollars.Enter vour equation in the first response boxPart B: John calculates that the total price will be $1500. How many square feet of carpet will he buy?Place your answer in the second response box”

Answer 1

Step-by-step explanation:

Given:

We are told that John pays $1.30 per square foot for the first 1000 square feet of carpet he buys. Then he pays $1.00 per additional square foot after the first 1000 square feet.

Required:

We are required to write an equation to represent the total price when he buys less than 1000 square feet.

Step-by-step solution;

Take note that he pays $1.30 per square foot for the first 1000 square feet. The amount spent, that is the price would be represented by p while, c would represent the amount of carpet to be bought.

Hence, for buying less than 1000 square feet;

`p=1.30c`

Next we note that John calculates that the total price would be $1500.

If John pays the amount of $1.30 for the first 1000 square feet, then he would have paid;

`p=1.30(1000)`
`p=1300`

However, we are told that John calculates a total of $1500. This simply means that he will buy more than 1000 square feet of carpet.

He is going to spend an extra $200 (that is 1500 minus 1300). The cost of any extra foot after the first 1000 is $1.00. That means;

`Extra\text{ }carpet=(200)/(1.00)`
`Extra\text{ }carpet=200ft^2`

That means John would be paying the sum of $1500 to buy 1,200 square feet of carpet.

ANSWER:

`\begin{gathered} Part\text{ }A: \\ p=1.30c \end{gathered}`
`\begin{gathered} Part\text{ }B: \\ 1200ft^2 \end{gathered}`