Leon cuts the length of a 9-foot board into two sections. Three times the length of the longer section is 3 feet more than 3 times the length of the shorter section.

Answer 1

We can set this up as a system of two equations in two variables to solve for the length of each section of the 9-foot board. If we let x = the shorter section and y = the longer section, our first equation will simply be that the 2 sections added together equal 9: x + y = 9

Our second equation will involve how the lengths are described in relation to each other, and this is where we build the equation based on the specific wording. "Three times the length of the longer section" will be translated as 3y. "Is" will be translated as =. "Three feet more than 3 times the length of the shorter section" will be translated as 3x + 3. So our 2nd equation will be 3y = 3x + 3.

At this point, you could easily solve by the substitution method since the y variable in the first equation can easily be isolated and then its expression inserted into the 2nd equation to replace the y. As always, once done solving, both values should be checked in both equations to verify that they work and are the correct lengths. Good luck!

Answer 2

3L = 3+3S

L+S = 9

L=9-S

3(9-S) = 3+3S

27-3S = 3+3S

6S = 24

S = 4 feet = Smaller piece's length

L = 9-4 = 5 feet = Longer piece's length

3(5) = 3+3(4)

15 = 3+12