Difference between revisions of "1992 AHSME Problems/Problem 7"

Revision as of 20:43, 2 March 2017

The ratio of $w$ to $x$ is $4:3$ , of $y$ to $z$ is $3:2$ and of $z$ to $x$ is $1:6$ . What is the ratio of $w$ to $y$ ?

$\text{(A) } 1:3\quad \text{(B) } 16:3\quad \text{(C) } 20:3\quad \text{(D) } 27:4\quad \text{(E) } 12:1$

$\fbox{B}$

Converting from ratios to fractions

$\frac{w}{x}=\frac{4}{3}$ , $\frac{y}{z}=\frac{3}{2}$ , $\frac{z}{x}=\frac{1}{6}$

$\frac{y}{x} \cdot \frac{z}{x} = \frac{3}{2} \cdot \frac{1}{6}$

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

$\frac{\frac{w}{x}}{\frac{y}{x}}=\frac{\frac{4}{3}}{\frac{1}{4}}$ $\frac{w}{y} = \frac{16}{3}$

$w$ to $x$ is $16:3$

1992 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

@@ Line 11: / Line 11: @@
 == Solution ==
 <math>\fbox{B}</math>
+Converting from ratios to fractions
+<math>\frac{w}{x}=\frac{4}{3}</math>,
+<math>\frac{y}{z}=\frac{3}{2}</math>,
+<math>\frac{z}{x}=\frac{1}{6}</math>
+<math>\frac{y}{x} \cdot \frac{z}{x} = \frac{3}{2} \cdot \frac{1}{6}</math>
+<math>\frac{y}{x} = \frac{1}{4}</math>
+<math>\frac{\frac{w}{x}}{\frac{y}{x}}=\frac{\frac{4}{3}}{\frac{1}{4}}</math>
+<math>\frac{w}{y} = \frac{16}{3}</math>
+<math>w</math> to <math>x</math> is <math>16:3</math>
 == See also ==