Better spelling
Weekly Problem 12 - 2010
Can Emily increase her average test score to more than $80$%? Find out how many more tests she must take to do so.
Can Emily increase her average test score to more than $80$%? Find out how many more tests she must take to do so.
Age
11 to 14
Challenge level
Problem
In Emily's first spelling test, she scored 1 mark out of 5, so she decided to work really hard to improve her scores.
If she scores full marks (5 out of 5) in all her tests after the first, how many more tests does she need to take, in order to increase her average to more than $80$%?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: four more tests
Using fractions
Initial score: $\dfrac15$
After 1 test: $\dfrac{1+5}{5+5}=\dfrac{6}{10}=60\%$
After 2 tests: $\dfrac{6+5}{10+5}=\dfrac{11}{15}\lt\dfrac{12}{15}$ which is equal to $80\%$
After 3 tests: $\dfrac{11+5}{15+5}=\dfrac{16}{20}=80\%$
After 4 tests: more than $80\%$
So she needs to take four more tests to obtain an average mark of more than $80$%.
Using averages
$\frac15=20\%$, get $100\%$ to reach target of $80\%$
$20\%$ is $60\%$ below $80\%$
$80\%$ is $20\%$ below $100\%$
$20\%\times3=60\%$
$20\%$ above three times to balance $60\%$ below
So after 3 more tests the average will be $80\%$
After the fourth test it will be above $80\%$