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?"

Answer 1

Sharon uses approximately 5.47 yards of ribbon for each small barrette and approximately 7.65 yards for each large barrette, after solving a system of equations and converting from meters to yards.

Step-by-step explanation:

To solve the problem, let's define x as the amount of ribbon Sharon uses for each small barrette and y as the ribbon used for each large barrette. We can then create two equations based on the given scenarios: for the Lakewood craft fair, 14 small barrettes and 12 large barrettes use 154 meters of ribbon, and for the Belleville craft fair, 13 small and 12 large barrettes use 149 meters of ribbon.

For Lakewood: 14x + 12y = 154

For Belleville: 13x + 12y = 149

To eliminate one variable, we can subtract the second equation from the first:

• (14x + 12y) - (13x + 12y) = 154 - 149
• 14x - 13x + 12y - 12y = 5
• x = 5

Now we know that Sharon uses 5 meters of ribbon for each small barrette. We can substitute this value into one of the original equations to find the value of y.

14(5) + 12y = 154

70 + 12y = 154

12y = 154 - 70

12y = 84

y = 7

Thus, Sharon uses 7 meters of ribbon for each large barrette. To convert meters into yards, we use the conversion factor 1 meter = 1.09361 yards.

x = 5 meters * 1.09361 yards/meter = 5.46805 yards (approximately 5.47 yards)

y = 7 meters * 1.09361 yards/meter = 7.65227 yards (approximately 7.65 yards)

Sharon uses approximately 5.47 yards of ribbon for each small barrette and approximately 7.65 yards for each large barrette.