Question

Mrs. Bradley bought 8 spools of thread. Each spool of purple thread is 3 meters long and each spool of orange thread is 4 meters long. If Mrs. Bradley bought 28 meters of thread in total, how many rolls of each color did she buy?Mrs. Bradley bought 8 spools of thread. Each spool of purple thread is 3 meters long and each spool of orange thread is 4 meters long. If Mrs. Bradley bought 28 meters of thread in total, how many rolls of each color did she buy?

Answer 1

4 purple thread spools and 4 orange thread spools

Explanation:

Let x = number of purple thread spools.

Let y = number of orange thread spools.

The total number of spools is 8, so the first equation is:

x + y = 8

Now we deal with the length of the threads.

Each spool of purple thread is 3 meters long, so x spools are 3x meters long. Each spool of orange thread is 4 meters long, so y spools are 4y meters long. The total length of the both threads is 3x + 4y. We are told the total amount of thread is 28 meters, so we have the second equation.

3x + 4y = 28

Now we have a system of 2 equations in 2 unknowns.

x + y = 8

3x + 4y = 28

We will solve it by the substitution method. Solve the first equation for x.

x = 8 - y

Now replace x in the second equation by 8 - y.

3x + 4y = 28

3(8 - y) + 4y = 28

24 - 3y + 4y = 28

24 + y = 28

y = 4

Substitute 4 for y in the first original equation and solve for x.

x + y = 8

x + 4 = 8

x = 4

We get x = 4, and y = 4.

x = number of purple thread spools

y = number of orange thread spools

Answer: 4 purple thread spools and 4 orange thread spools

Answer 2

Answer:she bought 4 rolls of each color.

Explanation:

Let x represent the number of rolls or spools of purple thread that Mrs. Bradley bought.

Let y represent the number of rolls or spools of orange thread that Mrs. Bradley bought.

Mrs. Bradley bought 8 spools of thread. This means that

x + y = 8

Each spool of purple thread is 3 meters long and each spool of orange thread is 4 meters long. If Mrs. Bradley bought 28 meters of thread in total, it means that

3x + 4y = 28

Substituting x = 8 - y into the equation, it becomes

3(8 - y) + 4y = 28

24 - 3y + 4y = 28

- 3y + 4y = 28 - 24

y = 4

Substituting y = 4 into x = 8 - y, it becomes

x = 8 - 4 = 4