Question
If \( 3: 8 \) is equivalent to \( (2 x+13): 72 \), then what is the value of \( x ? \)
Ask by French Chadwick. in the United Kingdom
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 7 \)
Solution
We can solve the problem by setting up a proportion based on the given ratios:
\[
\frac{3}{8} = \frac{2x + 13}{72}
\]
**Step 1: Cross-Multiply**
Multiply the numerator of one ratio by the denominator of the other:
\[
3 \times 72 = 8 \times (2x + 13)
\]
\[
216 = 16x + 104
\]
**Step 2: Solve for \( x \)**
Subtract 104 from both sides:
\[
216 - 104 = 16x
\]
\[
112 = 16x
\]
Divide both sides by 16:
\[
x = \frac{112}{16} = 7
\]
**Answer:** \( x = 7 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the proportion \( \frac{3}{8} = \frac{2x + 13}{72} \), we can cross-multiply to eliminate the fractions. This gives us: \[ 3 \times 72 = 8 \times (2x + 13) \] Calculating the left side: \[ 216 = 8(2x + 13) \] Now, distribute the 8 on the right side: \[ 216 = 16x + 104 \] Next, subtract 104 from both sides: \[ 216 - 104 = 16x \] This results in: \[ 112 = 16x \] To isolate \( x \), divide both sides by 16: \[ x = \frac{112}{16} \] Simplifying this gives: \[ x = 7 \] So, the value of \( x \) is \( 7 \).
