Linear Equations in Real-World Scenarios Quick Check

Question

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Question
A string is cut in two so that one section is 5 inches longer than the other. Twice the length of the longer section is three times the length of the shorter section. Write an equation that allows you to solve for the length of the shorter section. How long is the shorter section?(1 point)
Responses

15 inches
15 inches

10 inches
10 inches

20 inches
20 inches

12 inches

Answer 1

To solve the problem, let's define the lengths of the two sections of the string.

Let \( x \) be the length of the shorter section in inches. Then, the longer section will be \( x + 5 \) inches.

According to the problem, twice the length of the longer section is equal to three times the length of the shorter section. This can be expressed with the equation:

\[ 2(x + 5) = 3x \]

Now, let's solve for \( x \):

1. Distribute on the left side: \[ 2x + 10 = 3x \]

2. Subtract \( 2x \) from both sides: \[ 10 = 3x - 2x \] \[ 10 = x \]

Thus, the length of the shorter section, \( x \), is 10 inches.

The answer is: 10 inches.