Question

For the homecoming parade, the students of U-Math have created a colorful banner, 43 meters in length that is made of two pieces of parachute material. The short piece is 23 meters shorter than the long piece. Find the length of each piece.

Answer 1

The short piece is 10 meters long and the long piece is 33 meters long

Step-by-step explanation

Let the length of the shorter piece be x.

Let the length of the longer piece be y.

We have that the total length of the banner is 43 meters. This means that:

x + y = 43 ___(1)

The short piece is 23 meters shorter than the long piece. This means that:

x = y - 23 _____(2)

Now, we have a system of two simultaneous equations:

x + y = 43

x = y - 23

We can solve this by substitution.

Substitute the second equation into the first equation.

That is:

y - 23 + y = 43

Collect like terms:

y + y = 43 + 23

2y = 66

Divide through by 2:

y = 66 / 2

y = 33 m

Recall that:

x = y - 23

Therefore:

x = 33 - 23

x = 10 m

Therefore, the short piece is 10 meters long and the long piece is 33 meters long.