# Difference between revisions of "2006 AMC 10A Problems/Problem 3"

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<math> \mathrm{(A) \ } 15\qquad \mathrm{(B) \ } 18\qquad \mathrm{(C) \ } 20\qquad \mathrm{(D) \ } 24\qquad \mathrm{(E) \ } 50 </math> | <math> \mathrm{(A) \ } 15\qquad \mathrm{(B) \ } 18\qquad \mathrm{(C) \ } 20\qquad \mathrm{(D) \ } 24\qquad \mathrm{(E) \ } 50 </math> | ||

== Solution == | == Solution == | ||

+ | We can create the ratio | ||

+ | |||

+ | <math>\frac{3}{5}=\frac{x}{30}</math> | ||

+ | |||

+ | Where ''x'' is Mary's age. Simplfying yields | ||

+ | |||

+ | <math>(3)(30)=5x\Longrightarrow 90=5x\Longrightarrow x=18, (B)</math> | ||

== See Also == | == See Also == | ||

*[[2006 AMC 10A Problems]] | *[[2006 AMC 10A Problems]] |

## Revision as of 13:31, 3 July 2006

## Problem

The ratio of Mary's age to Alice's age is 3:5. Alice is 30 years old. How many years old is Mary?

## Solution

We can create the ratio

Where *x* is Mary's age. Simplfying yields