Difference between revisions of "1985 AJHSME Problem 21"
Coolmath34 (talk | contribs) (Created page with "== Problem == Mr. Green receives a <math>10\% </math> raise every year. His salary after four such raises has gone up by what percent? <math>\text{(A)}\ \text{less than }40...") |
(logic) |
||
| Line 7: | Line 7: | ||
== Solution == | == Solution == | ||
If Mr. Green's original salary is \$100, then his salary after four raises is <math>(100)(1.1)^4 = 146.41.</math> This is an increase of 46.41%, so the answer is <math>\text{(E)}\ \text{more than }45\%. </math> | If Mr. Green's original salary is \$100, then his salary after four raises is <math>(100)(1.1)^4 = 146.41.</math> This is an increase of 46.41%, so the answer is <math>\text{(E)}\ \text{more than }45\%. </math> | ||
| + | |||
| + | (note: this number can be calculated by recalling powers of <math>11</math> appear in Pascal's Triangle: <math>11^4</math> appears on the fourth row, which is <math>1 4 6 4 1</math> meaning that <math>11^4=14641</math>, so <math>1.1^4=1.4641</math>. | ||
Latest revision as of 10:48, 13 December 2024
Problem
Mr. Green receives a 
raise every year. His salary after four such raises has gone up by what percent?
Solution
If Mr. Green's original salary is $100, then his salary after four raises is 
This is an increase of 46.41%, so the answer is 
(note: this number can be calculated by recalling powers of 
appear in Pascal's Triangle: 
appears on the fourth row, which is 
meaning that 
, so 
.
