# Calculating percentages of a percent of a percent

A student is taking a class where $40\%$ of his or her grade is based on homework and the remaining $60\%$ is based on tests. There are a total of 12 homework assignments and 4 tests. The student completes $9/12$ assignments with a perfect score and all 4 tests with a perfect score. What is his final grade? I first converted the homework assignments into a decimal $$9/12 = .75$$ since their homework is 40% of their grade: $$.75 * .4 = .3$$ which I then added to the final quiz percentage to get a total grade for the class: $$.3 + .6 = .9$$ $$.9 * 100 = 90$$

The student completed the class with an A(90%), however I'm not sure this calculation is correct. Can someone please verify?

• alan - for some reason your first use of '40 percent' is showing as 40. Might make a quick edit to fix this.
– 123
Nov 16 '14 at 21:36
• I would greatly appreciate that, I am unsure how to display percent signs with MathJax. Nov 16 '14 at 21:37
• fixed it. I had to make a few arbitrary changes since there is a minimum amount of characters I must change to submit an edit.
– 123
Nov 16 '14 at 21:40
• @AlanZ2223: to display percent signs in MathJax you need to escape them with a backslash. so 60\% gives $60\%$ when put between dollar signs. That is generally true, for dollar signs, braces, etc Nov 16 '14 at 21:40
• It is correct.${}$ Nov 16 '14 at 21:40

You are correct. Another way to think about it is to have $100$ points available. Each test is $\frac 14$ of $60\%$ of $100$ or $15$ points. Each homework is $\frac 1{12}$ of $40\%$ of $100$ or $\frac {10}3$ points. The student has accumulated $4 \cdot 15 + 9 \cdot \frac {10}3=90$ points.