Question

The sum of x, y, and z is 98. The ratio of x : y = 2 : 3, and the ratio of y : z = 5 : 8. What is the value of y?

• A. 30
• B. 20
• C. 48
• D. 58

Hint:

To combine two ratios, make the common term equal using LCM and then merge the ratios into a three-variable ratio.

Answer 1

The Correct Option is A

Step 1: Write the two ratios.
We are given $x : y = 2 : 3$ and $y : z = 5 : 8$, and we must combine them through the common term $y$.
Step 2: Make $y$ match.
The value of $y$ is $3$ in the first ratio and $5$ in the second; their LCM is $15$.
Step 3: Scale each ratio.
Multiply the first by $5$ to get $x : y = 10 : 15$, and the second by $3$ to get $y : z = 15 : 24$.
Step 4: Form the combined ratio.
Now $x : y : z = 10 : 15 : 24$.
Step 5: Use the total.
The parts add to $10 + 15 + 24 = 49$, and the sum is $98$, so one part equals $98 \div 49 = 2$.
Step 6: Compute $y$.
$y = 15 \times 2 = 30$.
\[ \boxed{30} \]