Ask Question
15 October, 19:34

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?

+1
Answers (2)
  1. 15 October, 20:22
    0
    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
  2. 15 October, 21:32
    0
    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
Know the Answer?