Math Competition Problems - Problem of the Week - 19
Updated: Oct 18, 2020
Ryan got 80% of the problems correct on a 25-problem test, 90% on a 40-problem test, and 70% on a 10-problem test. What percent of all the problems did Ryan answer correctly? - AMC 8 2010
For almost all the beginners problems on percentages are the most troublesome ones. So let's look at how to solve this.
Let's look at what is given.
Ryan got 80% of the problems correct on a 25-problem test. Which means he got
80/100 * 25 which is 20 questions correct. So he scored 20/25 on his first test.
He then got 90% on a 40-problem test. Which means he got 90/100 * 40= 36 questions correct. So he scored 36/40 on his next test.
At last he got 70% on a 10-problem test. Which means he got 70/100 * 10 = 7questions correct. So he scored 7/10 on his last test.
To get the percent of all the problems did Ryan answer correctly - we need to do
No. of problems correct/ Total number of questions * 100
The total number of problems he got right is 20+36+7= 63
Total number of questions = 25+40+10=75
So fraction of questions he got right = 63/75 which simplifies to 21/25 and as a percentage it will be 21/25 * 100 which is 84%
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