Question

X is greater than y by 12 and Z is less than y by 8. If the ratio of x:z is 9:4. What is the value of Z?
A)12 B) 16 C) 20 D) 36 E) none of these

Answer 1

B

Express x and z in terms of y

x = y + 12 and z = y - 8

Express the ratio x : z as equivalent fractions

$\frac{9}{4}$ = $\frac{y+12}{y-8}$ ( cross-multiply )

9(y - 8) = 4(y + 12) ( distribute both sides )

9y - 72 = 4y + 48 ( subtract 4y from both sides )

5y - 72 = 48 ( add 72 to both sides )

5y = 120 ( divide both sides by 5 )

y = 24 ⇒ z = 24 - 8 = 16