2000 CEMC Gauss (Grade 8) Problems/Problem 10: Difference between revisions
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{{Duplicate|[[2000 CEMC Gauss (Grade 8) Problems|2000 CEMC Gauss (Grade 8) #10]] and [[2000 CEMC Gauss (Grade 7) Problems|2000 CEMC Gauss (Grade 7) #13]]}} | |||
==Problem== | ==Problem== | ||
Karl had his salary reduced by <math>10\%</math>. He was later promoted and his salary was increased by <math>10\%</math>. If his initial salary was <math>\$20~000</math>, what is his present salary? | Karl had his salary reduced by <math>10\%</math>. He was later promoted and his salary was increased by <math>10\%</math>. If his initial salary was <math>\$20~000</math>, what is his present salary? | ||
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~anabel.disher | ~anabel.disher | ||
{{CEMC box|year=2000|competition=Gauss (Grade 8)|num-b=9|num-a=11}} | |||
{{CEMC box|year=2000|competition=Gauss (Grade 7)|num-b=12|num-a=14}} | |||
Latest revision as of 12:54, 20 October 2025
- The following problem is from both the 2000 CEMC Gauss (Grade 8) #10 and 2000 CEMC Gauss (Grade 7) #13, so both problems redirect to this page.
Problem
Karl had his salary reduced by 
. He was later promoted and his salary was increased by . If his initial salary was 
, what is his present salary?
Solution 1
If Karl's salary was reduced by , that means that 
of the initial salary was remaining before the promotion. Thus, he had 
left.
After his promotion, this was then raised by , so his salary is 
times what it was before he got promoted.
~anabel.disher
Solution 2
Let 
be the initial salary. After it was reduced, he had 
for his salary.
After his promotion, he then had 
for the salary.
Since we know the initial salary was , we can plug-in 
. We then have:
~anabel.disher
| 2000 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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 | ||
| CEMC Gauss (Grade 8) | ||
| 2000 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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 | ||
| CEMC Gauss (Grade 7) | ||
