Question
Write the following as an equation. Then solve.
Twice the sum of a number and 5 is equal to three times the difference of the number and 5. Find the number.
Question content area bottom
Part 1
Let x be the unknown number. Write an equation. Choose the correct answer below.
A.2 left parenthesis x minus 5 right parenthesis equals 3 left parenthesis x minus 5 right parenthesis
2 left parenthesis x minus 5 right parenthesis equals 3 left parenthesis x minus 5 right parenthesis
B.2 left parenthesis x plus 5 right parenthesis equals 3 left parenthesis x plus 5 right parenthesis
2 left parenthesis x plus 5 right parenthesis equals 3 left parenthesis x plus 5 right parenthesis
C.2 left parenthesis x minus 5 right parenthesis equals 3 left parenthesis x plus 5 right parenthesis
2 left parenthesis x minus 5 right parenthesis equals 3 left parenthesis x plus 5 right parenthesis
D.2 left parenthesis x plus 5 right parenthesis equals 3 left parenthesis x minus 5 right parenthesis
2 left parenthesis x plus 5 right parenthesis equals 3 left parenthesis x minus 5 right parenthesis
Twice the sum of a number and 5 is equal to three times the difference of the number and 5. Find the number.
Question content area bottom
Part 1
Let x be the unknown number. Write an equation. Choose the correct answer below.
A.2 left parenthesis x minus 5 right parenthesis equals 3 left parenthesis x minus 5 right parenthesis
2 left parenthesis x minus 5 right parenthesis equals 3 left parenthesis x minus 5 right parenthesis
B.2 left parenthesis x plus 5 right parenthesis equals 3 left parenthesis x plus 5 right parenthesis
2 left parenthesis x plus 5 right parenthesis equals 3 left parenthesis x plus 5 right parenthesis
C.2 left parenthesis x minus 5 right parenthesis equals 3 left parenthesis x plus 5 right parenthesis
2 left parenthesis x minus 5 right parenthesis equals 3 left parenthesis x plus 5 right parenthesis
D.2 left parenthesis x plus 5 right parenthesis equals 3 left parenthesis x minus 5 right parenthesis
2 left parenthesis x plus 5 right parenthesis equals 3 left parenthesis x minus 5 right parenthesis
Answers
GPT-4o mini
Let's begin by translating the given information into an equation.
The problem states: "Twice the sum of a number and 5 is equal to three times the difference of the number and 5."
Let's denote the unknown number as \( x \).
- The sum of the number and 5 is \( x + 5 \).
- Twice the sum is \( 2(x + 5) \).
- The difference of the number and 5 is \( x - 5 \).
- Three times the difference is \( 3(x - 5) \).
Now we can set up the equation based on the description:
\[
2(x + 5) = 3(x - 5)
\]
Now, looking at the options provided:
- Option A: \( 2(x - 5) = 3(x - 5) \)
- Option B: \( 2(x + 5) = 3(x + 5) \)
- Option C: \( 2(x - 5) = 3(x + 5) \)
- Option D: \( 2(x + 5) = 3(x - 5) \)
The correct option based on our equation \( 2(x + 5) = 3(x - 5) \) is **Option D**.
Next, let’s solve the equation \( 2(x + 5) = 3(x - 5) \).
1. Distribute both sides:
\[
2x + 10 = 3x - 15
\]
2. Rearrange the equation to isolate \( x \):
\[
10 + 15 = 3x - 2x
\]
\[
25 = x
\]
Thus, the number is \( \boxed{25} \).
The problem states: "Twice the sum of a number and 5 is equal to three times the difference of the number and 5."
Let's denote the unknown number as \( x \).
- The sum of the number and 5 is \( x + 5 \).
- Twice the sum is \( 2(x + 5) \).
- The difference of the number and 5 is \( x - 5 \).
- Three times the difference is \( 3(x - 5) \).
Now we can set up the equation based on the description:
\[
2(x + 5) = 3(x - 5)
\]
Now, looking at the options provided:
- Option A: \( 2(x - 5) = 3(x - 5) \)
- Option B: \( 2(x + 5) = 3(x + 5) \)
- Option C: \( 2(x - 5) = 3(x + 5) \)
- Option D: \( 2(x + 5) = 3(x - 5) \)
The correct option based on our equation \( 2(x + 5) = 3(x - 5) \) is **Option D**.
Next, let’s solve the equation \( 2(x + 5) = 3(x - 5) \).
1. Distribute both sides:
\[
2x + 10 = 3x - 15
\]
2. Rearrange the equation to isolate \( x \):
\[
10 + 15 = 3x - 2x
\]
\[
25 = x
\]
Thus, the number is \( \boxed{25} \).