Q17: The sum of the numbers x, y, and z

October 15, 2026

2018 Test A Math · Question 17 of 57

The sum of the numbers x, y, and z is 50. The ratio of x to y is 1:4, and the ratio of y to z is 4:5. What is the value of y ?

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Correct answer: D

Since both ratios have $y$ in common, solve for $x$ and $z$ in terms of $y$ in both equations. Using $x:y=1:4$ , solve for $x$ in terms of $y$ .

$frac{x}{y}=frac{1}{4}$

$x=frac{y}{4}$

Using the ratio terms of $y$ :

$frac{y}{z}=frac{4}{5}$

$z=frac{5}{4}y$

The question states $x+y+z=50$ . Substitute from the two equations above and solve for $y$ .

$frac{1}{4}y+y+frac{5}{4}y=50$

$4(frac{1}{4}y+y+frac{5}{4}y=50)4$

$y+4y+5y=200$

$10y=200$

$y=20$