Answer:she bought 4 rolls of each color.
Step-by-step 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
Answer:
4 purple thread spools and 4 orange thread spools
Step-by-step 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
