Question
\begin{tabular}{l} Calculate \( x \) for each ratio \\ \( \qquad 21=x: 7 \) \\ \hline (B) \( 15: 25=32 \)\end{tabular}
Ask by George Johnson. in South Africa
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 147 \) and \( y = \frac{160}{3} \) or approximately \( 53.33 \).
Solution
Sure, let's solve each ratio step by step.
---
### **1. Solve for \( x \) in the ratio \( 21 = \frac{x}{7} \):**
The given ratio is:
\[
21 = \frac{x}{7}
\]
To find \( x \), multiply both sides of the equation by 7:
\[
x = 21 \times 7
\]
\[
x = 147
\]
**Answer:** \( x = 147 \)
---
### **2. Solve the ratio \( \frac{15}{25} = \frac{32}{y} \):**
Assuming the ratio is:
\[
\frac{15}{25} = \frac{32}{y}
\]
To find \( y \), cross-multiply:
\[
15y = 25 \times 32
\]
\[
15y = 800
\]
Now, divide both sides by 15:
\[
y = \frac{800}{15}
\]
\[
y = \frac{160}{3} \quad \text{or approximately} \quad 53.\overline{3}
\]
**Answer:** \( y = \frac{160}{3} \) or approximately \( 53.33 \)
---
If you have any more ratios or need further clarification, feel free to ask!
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Simplify this solution Extra Insights
To solve the equation \( 21 = x:7 \), we can rewrite it in a more familiar form. A ratio can be expressed as a fraction, so we can write it as \( \frac{x}{7} = 21 \). To find \( x \), we can cross-multiply: \( x = 21 \times 7 \). This gives us \( x = 147 \). For the second ratio \( 15:25 = 32 \), we need to set up a proportion. We can rewrite it as \( \frac{15}{25} = \frac{32}{y} \). By cross-multiplying, we get \( 15y = 25 \times 32 \). Solving for \( y \) gives us \( y = \frac{800}{15} \), which reduces to \( y \approx 53.33 \). So, the answers are \( x = 147 \) and \( y \approx 53.33 \).
