Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Sharon is using ribbon to create girls' hair barrettes. For a craft fair in Lakewood, she made 14 small barrettes and 12 large barrettes, using a total of 154 meters of ribbon. Then, for another craft fair in Belleville, she made 13 small barrettes and 12 large barrettes, which used a total of 149 meters. How many yards of ribbon does Sharon use for each?​

A. Sharon uses 6 meters of ribbon for each small barrette and 8 meters of ribbon for each large.
B. Sharon uses 3 meters of ribbon for each small barrette and 6 meters of ribbon for each large barrette.
C. Sharon uses 8 meters of ribbon for each small barrette and 4 meters of ribbon for each large barrette.
D. Sharon uses 10 meters of ribbon for each small barrette and 9 meters of ribbon for each large barrette.

Answer 1

To solve this problem, we can set up a system of equations using the given information about the number of barrettes and the total length of ribbon used. By solving the system of equations using elimination, we can find the values of x and y, representing the amount of ribbon used for each small and large barrette. However, the given answer options do not provide the correct solution.

Step-by-step explanation:

To write a system of equations to describe the situation, let x represent the amount of ribbon used for each small barrette (in meters) and let y represent the amount of ribbon used for each large barrette (in meters). We can set up the following system of equations:

Equation 1: 14x + 12y = 154

Equation 2: 13x + 12y = 149

To solve this system of equations using elimination, we can multiply Equation 1 by 13 and Equation 2 by 14 to eliminate the variable x:

Multiplying Equation 1 by 13: 182x + 156y = 2002

Multiplying Equation 2 by 14: 182x + 168y = 2086

By subtracting the two equations, we can eliminate the variable x:

(182x + 168y) - (182x + 156y) = 2086 - 2002

12y - 6y = 84

6y = 84

y = 14

Substituting the value of y into either Equation 1 or Equation 2, we can solve for x:

Using Equation 1: 14x + 12(14) = 154

14x + 168 = 154

14x = -14

x = -1

Therefore, the solution to the system of equations is x = -1 and y = 14. Since we cannot have negative lengths of ribbon, the correct answer is not provided in the options given.