Difference between revisions of "1988 AHSME Problems/Problem 8"
(Created page with "==Problem== If <math>\frac{b}{a} = 2</math> and <math>\frac{c}{b} = 3</math>, what is the ratio of <math>a + b</math> to <math>b + c</math>? <math>\textbf{(A)}\ \frac{1}{3}\qqu...") |
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==Solution== | ==Solution== | ||
| − | + | Since we are finding ratios, it would be helpful to put everything in terms of one variable. Since <math>b</math> is in both equations, that would be a place to start. | |
| − | + | We manipulate the equations yielding <math>\frac{b}{2}=a</math> and <math>c=3b</math>. Since we are asked to find the ratio of <math>a+b</math> to <math>b+c</math>, we need to find <math>\frac{a+b}{b+c}</math>. We found the <math>a</math> and <math>c</math> in terms of <math>b</math> so that means we can plug them in. We have: <math>\frac{\frac{b}{2}+b}{b+3b}=\frac{\frac{3}{2}b}{4b}=\frac{3}{8}</math>. Thus the answer is <math>\frac{3}{8} \implies \boxed{\text{B}}</math>. | |
== See also == | == See also == | ||
Revision as of 07:30, 31 August 2015
Problem
If 
and 
, what is the ratio of 
to 
?
Solution
Since we are finding ratios, it would be helpful to put everything in terms of one variable. Since 
is in both equations, that would be a place to start.
We manipulate the equations yielding 
and 
. Since we are asked to find the ratio of 
to 
, we need to find 
. We found the 
and 
in terms of so that means we can plug them in. We have: 
. Thus the answer is 
.
See also
| 1988 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
