Question

A string of outdoor lights is formed from strings that are 5 feet long and 11 feet long. If a total of 14 strings of lights are used and the combined length of all the strings is 106 feet, how many strings of each length were used?

Answer 1

There are 8 strings that are 5 feet long and 6 strings that are 11 feet long.

Step-by-step explanation:

Let x be the number of strings that are 5 feet long, and y be the number of strings that are 11 feet long.

From the given information, we can set up the following equations:

5x + 11y = 106 (equation 1)

x + y = 14 (equation 2)

We can solve this system of equations using substitution or elimination method. Let's use the elimination method:

Multiply equation 2 by 5 to make the coefficients of x the same:

5x + 5y = 70 (equation 3)

Subtract equation 3 from equation 1:

5x + 11y - (5x + 5y) = 106 - 70

6y = 36

y = 6

Substitute y = 6 into equation 2:

x + 6 = 14

x = 8

Therefore, there are 8 strings that are 5 feet long and 6 strings that are 11 feet long.