Question

You cut a piece of ribbon into two pieces so thatone piece is 4 inches longer than the other. Thelonger piece is 3 times as long as the shorter piece.a. How long is each piece of ribbon?b. How long was the original ribbon?

Answer 1

Given:

One piece is 4 inches longer than the other. We have the equation:

L = S + 4...........................................equation 1

The longer piece is 3 times as long as the shorter piece. We have the equation:

L = 3S................................................equation 2

Where S represents the shorter piece and L represents the longer piece.

Thus, we have the system of equations:

L = S + 4

L = 3S

Substitute for L in equation 2 from equation 1.

We have:

L = S + 4 = 3S

S + 4 = 3S

Subtract S from both sides:

S - S + 4 = 3S - S

4 = 2S

Divide both sides by 2:

`\begin{gathered} (4)/(2)=(2S)/(2) \\ \\ 2=S \\ \\ S=2 \end{gathered}`

The length of the shorter piece is 2 inches

To find the length of the longer piece, substitute 2 fo S in either equation 1 or 2.

From equation 1:

L = S + 4

L = 2 + 4 = 6

The length of the longer piece is 6 inches.

Therefore, the shorter piece is 2 in long, while the longer piece is 6 in long.

b) To find the length of the orginal ribbon, add the length of the shorter piece and that of the longer piece.

Length of original ribbon = 2 + 6 = 8 inches.

Therefore, the original ribbon is 8 inches long.

ANSWER:

a) Length of longer ribbon = 6 in

Length of shorter ribbon = 2 in

b) Length of original ribbon = 8 in