Question

If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?

• A. 3:4
• B. 5:6
• C. 15:24
• D. 5:8

Hint:

A faster method is to treat the ratios as fractions. \( \frac{A}{B} = \frac{3}{4} \) and \( \frac{B}{C} = \frac{5}{6} \). To find \( \frac{A}{C} \), multiply the two fractions: \( \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} = \frac{3}{4} \times \frac{5}{6} = \frac{15}{24} = \frac{5}{8} \).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
To find the ratio of A to C, we need to combine the two given ratios. The common term is B. We must make the value corresponding to B the same in both ratios by finding the least common multiple (LCM).
Step 2: Detailed Explanation:
The given ratios are:
\[ A : B = 3 : 4 \] \[ B : C = 5 : 6 \] The values for B in the two ratios are 4 and 5. The LCM of 4 and 5 is 20.
Step 2a: Adjust the first ratio.
To make the B term equal to 20, we multiply the entire first ratio by 5.
\[ A : B = (3 \times 5) : (4 \times 5) = 15 : 20 \] Step 2b: Adjust the second ratio.
To make the B term equal to 20, we multiply the entire second ratio by 4.
\[ B : C = (5 \times 4) : (6 \times 4) = 20 : 24 \] Step 2c: Combine the ratios.
Now that B is 20 in both ratios, we can write a combined ratio for A:B:C.
\[ A : B : C = 15 : 20 : 24 \] Step 2d: Find the ratio of A to C.
From the combined ratio, we can see the relationship between A and C.
\[ A : C = 15 : 24 \] This ratio can be simplified by dividing both parts by their greatest common divisor, which is 3.
\[ A : C = \frac{15}{3} : \frac{24}{3} = 5 : 8 \] Step 3: Final Answer:
The ratio of A to C is 5:8.