Difference between revisions of "1991 AHSME Problems/Problem 9"
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\text{(E) } \left(i+j+\frac{i+j}{100}\right)\%</math> | \text{(E) } \left(i+j+\frac{i+j}{100}\right)\%</math> | ||
| − | == Solution ==The scale factors for the increases are <math>1+\frac{i}{100}</math> and <math>1+\frac{j}{100}</math>, so the overall scale factor is <math>(1+\frac{i}{100})(1+\frac{j}{100}) = 1 + \frac{i}{100} + \frac{j}{100} + \frac{ij}{100^2}</math>. To convert this to a percentage, we subtract 1 and then multiply by 100, giving <math>i + j + \frac{ij}{100} | + | == Solution == |
| + | <math>\fbox{D}</math> The scale factors for the increases are <math>1+\frac{i}{100}</math> and <math>1+\frac{j}{100}</math>, so the overall scale factor is <math>(1+\frac{i}{100})(1+\frac{j}{100}) = 1 + \frac{i}{100} + \frac{j}{100} + \frac{ij}{100^2}</math>. To convert this to a percentage, we subtract 1 and then multiply by 100, giving <math>i + j + \frac{ij}{100}.</math> | ||
== See also == | == See also == | ||
Revision as of 12:28, 14 March 2023
Problem
From time 
to time 
a population increased by 
, and from time to time 
the population increased by 
. Therefore, from time to time the population increased by
Solution
The scale factors for the increases are 
and 
, so the overall scale factor is 
. To convert this to a percentage, we subtract 1 and then multiply by 100, giving 
See also
| 1991 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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. 
