Difference between revisions of "1973 AHSME Problems/Problem 12"
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==See Also== | ==See Also== | ||
| − | {{AHSME | + | {{AHSME 30p box|year=1973|num-b=11|num-a=13}} |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Latest revision as of 13:58, 20 February 2020
Problem
The average (arithmetic mean) age of a group consisting of doctors and lawyers in 40. If the doctors average 35 and the lawyers 50 years old, then the ratio of the numbers of doctors to the number of lawyers is
Solution
Let 
be the number of doctors and 
be the number of lawyers. The average age of the doctors is 
, so the sum of the doctors' ages is 
. The average age of the lawyers is 
, so the sum of the lawyers' ages is 
. With the two information, we can write an equation.
![\[\frac{35d+50l}{d+l} = 40\]](http://latex.artofproblemsolving.com/8/2/5/8251598b3f225d7a72a5e59261d16cc60067d37b.png)
![\[35d+50l=40d+40l\]](http://latex.artofproblemsolving.com/e/2/b/e2b7f9bd60ab390b0f40e260ed881ff74eac7496.png)
![\[10l=5d\]](http://latex.artofproblemsolving.com/d/d/4/dd4adcb8524d14ef363063bdba0945667b1d2d91.png)
![\[\frac{d}{l} = 2\]](http://latex.artofproblemsolving.com/c/a/f/caf459536e694d98609b8b4ccbd418f73a261d1b.png)
The ratio of the number of doctors to the number of lawyers is 
.
See Also
| 1973 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 • 31 • 32 • 33 • 34 • 35 | ||
| All AHSME Problems and Solutions | ||
