Algeba Equation

Question

A 26 foot board is cut into three pieces. The second piece measures one more than three times the first. The third piece measures four less than the second piece. Find the measure of the first piece.

Answer 1

f represents the first piece

3f + 1 represents the second piece

3f + 1 - 4 represents the third piece

f + 3f +1 + 3f - 3 = 26

Can you solve for f and answer?

Answer 2

The first thing we want to do is note that the first piece (A), the second piece (B) and the third (C) equal 26 when added together, that is A + B + C = 26..... (1)

The other piece of information we know is that

B = 1 + 3A..... (2)

C = B - 4..... (3)

We want to substitute C and B into (1) to get rid of the other letters so that we're left with only A.

A + B + C = 26 --- Substitute C out for B - 4

A + B + (B - 4) = 26 --- Simplify

A + 2B - 4 = 26 --- Add 4 to both sides

A + 2B = 30 --- Substitute B out for 1 + 3A

A + 2(1 + 3A) = 30 --- Simplify

A + 2 + 6A = 30 --- Simplify and subtract 2 from both sides

7A = 28 --- Divide by 7

A = 4

CHECK:

A = 4

B = 1 + 3A = 1 + 3(4) = 13

C = B - 4 = 13 - 4 = 9

A + B + C = 4 + 13 + 9 = 26