
Problem (for those who can't read the picture):
Willy Makit is participating at the local level of a decathlon in which he competes in 10 events. In each event the maximum possible score is 10 points. To advance to the regional level of the decathlon a competitor must earn a minimum total score of 75 points.
On the first five events, Willy had an average score of 6.8. On the next three events his average score was 7.2.
What must Willy's average on his final two events in order to have a total score of exactly 75 points?
Solution:
Step 1:
What I know:
("-"=info about the question, "*"=important numbers/parts for the question needed to solve the problem, " "=ANYTHING important/pay special attention to it)
-Willy Makit is participating at a decathlon where he competes in 10 different events
-In each even the maximum possible score is 10 points
-To advance to the regional level a competitor must get a minimum 75 points
*On the first 5 events, Willy had an average of 6.8
*On the next 3 events, his average score was 7.2
What I want to know:
*What must Willy's average on his final 2 events in order to have a total score of exactly 75 points?
Step 2:
Strategy:
First thing I need to do is find the average along with the both sides of the numbers. In fact, that is pretty much what we need to do. Once we find out the average of both the first 5 events then the next 3 events and subtract it from 75.0. Then later divide it by 2 so that we can find out how many points are needed as minimum to pass to the next level.
Step 3:
Carry out the plan:
To determine an average, we add the numbers together and divide the total by the number of numbers.
Average =Total÷Number of Numbers
So to determine the total we would multiply the average by the number of numbers.
Total = Average × Number of Numbers
Total Score for First 5 Events = 6.8 × 5 = 34.0
Total Score for Next 3 Events = 7.2 × 3 = 21.6
Total Score to Move On = 75.0
Total Score Needed for Last Two Events = 75.0 − 34.0 − 21.6 = 19.4
Average Score for Final 2 Events = 19.4 ÷ 2 = 9.7
Step 4:
Recheck:
9.7×2=19.4
75.0-19.4=55.6
55.6-21.6=34.0 OR 55.6-34.0=21.6
34.0÷5=6.8 OR 34.0÷6.8=5
21.6÷3=7.2 OR 21.6÷7.2=3 (It is confirmed that Willy Makit needs at least 9.7 on her last 2 competitions to pass to the regional level of the decathlon)
Step 5:
Conclusion:
Willy Makit needs at least 9.7 on her last 2 competitions to pass to the regional level of the decathlon.













