Question

A store had five different lengths of extension cords for sale. Four of the lengths were 9 feet, 10 feet, 12 feet, and 8 feet. The range of the lengths of all the extension cords was 6 feet. Which could be the length of the fifth size of extension cords?A. 18 feetB. 15 feetC. 2 feetD. 6 feet

Answer 1

The range is the difference between the greatest and smallest value. Now, if 12 feet is the greatest length of extension cord, we have:

`\begin{gathered} \text{range = greatest length - smallest length} \\ 6ft=12ft-\text{ smallest length} \\ \text{ Subtract 12ft from both sides of the equation} \\ -12ft+6ft=-12ft+12ft-\text{ smallest length} \\ -6ft=-\text{ smallest length} \\ \text{ Multiply by -1 from both sides of the equation} \\ -1\cdot-6ft=-1\cdot-\text{ smallest length} \\ 6ft=\text{ smallest length} \end{gathered}`

Therefore, the length of the fifth size of extension cords could be 6 feet.