Math Competition Problems - Problem of the Week - 19

Updated: Oct 18

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.


Solution:

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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