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
12 inches
12 inches
15 inches
15 inches
20 inches
20 inches
10 inches
Let's represent the length of the shorter section as x.
According to the problem, the longer section is 5 inches longer than the shorter section, so its length can be represented as x + 5.
Twice the length of the longer section is three times the length of the shorter section. This can be written as:
2(x + 5) = 3x
Now we can solve this equation for x:
2x + 10 = 3x
10 = 3x - 2x
10 = x
Therefore, the length of the shorter section is 10 inches.
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Let's call the length of the shorter section "x" inches.
According to the problem, the longer section is 5 inches longer than the shorter section. So, the length of the longer section would be "x+5" inches.
Twice the length of the longer section is three times the length of the shorter section. This can be represented by the equation:
2(x+5) = 3x
Now, let's solve this equation to find the value of "x":
2x + 10 = 3x
Subtracting 2x from both sides:
10 = x
Therefore, the length of the shorter section is 10 inches.
To solve this problem, let's start by assigning variables. Let's call the length of the shorter section "x".
According to the problem, the longer section is 5 inches longer than the shorter section, so its length can be represented as "x + 5".
The problem also states that twice the length of the longer section is three times the length of the shorter section. Mathematically, this can be written as:
2*(x + 5) = 3*x
Now we can solve this equation to find the value of "x".
First, distribute the 2 to the terms inside the parentheses:
2x + 10 = 3x
Next, subtract 2x from both sides to get all the x terms on one side of the equation:
10 = x
Therefore, the length of the shorter section is 10 inches.