Xis 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

B

Express x and z in terms of y

x = y + 12 and z = y - 8

Express the ratio x : z as equivalent fractions

= ( 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