A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the ot

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A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the other. How long should the pieces be?

The key phrase in this problem is two pieces.

Declare Variables:

• Let the short piece length be s
• Let the long piece length be l

We're given the following

1. s = l - 10
2. s + l = 98 (Because the two pieces add up to 98)

Substitute equation (1) into equation (2) for s:
l - 10+ l = 98

Group like terms:
2l - 10 = 98

Solve for l in the equation 2l - 10 = 98

Step 1: Group constants:
We need to group our constants -10 and 98. To do that, we add 10 to both sides
2l - 10 + 10 = 98 + 10

Step 2: Cancel 10 on the left side:
2l = 108

Step 3: Divide each side of the equation by 2
2l/2 = 108/2
l = 54

To solve for s, we substitute l = 54 into equation (1):
s = 54 - 10
s = 44

Check our work:
The shorter piece is 10 inches shorter than the longer piece since 54 - 44 = 10

Second check: Do both pieces add up to 98
54 + 44 ? 98
98 = 98