A state department of education, as a question on the public-release form of a statewide standardized test, released a question to the public in which eighth-grade students have to determine how many students are now in a school that had 80 students last year if the school has 10 percent more students this year than last year.
First things first. What is 10% of 80? Well, we could do it the long way and multiply 80 × 10%, which means 80 × 0.10, since “percent” means “out of 100.” That is why we should write 10% as 10 hundredths, or 0.10.
That comes to 8, but we could have saved ourselves a step with this problem. We know that 10 percent of any number is just the number that you get when you move the decimal point one place to the left:
And if 10 percent of 80 is 8 and the problem says there are 10% more students this year than last, that means there are 8 more students this year than there were last year. Last year, the school had 80 students, and this year we have 8 more students.
Therefore there are 88 students at the school this year, which is 10 percent more than there were last year.
This problem is similar to finding the tax on a sale. For instance, let’s say your double cheeseburger costs $1 (that is the price for a double cheeseburger at McDonald’s and at similar fast-food restaurants) and you buy two of them along with a Diet Coke that costs $1.50, bringing your total to $1 + $1 + $1.50 = $3.50.
If the tax rate where you live is 8 percent, how much will you pay?
As above, we put first things first: What is 8% of $3.50? Since 8 percent means “8 hundredths,” we multiply the total cost of the food (3.50) by 0.08. And once we know how much the 8-percent tax will be, we add it to the 3.50, shown below:
That is to say, .28 is 8 percent of 3.50. Tax always adds to the actual purchase price. In other words, first we multiply to find the amount of just the tax, and then we add that tax amount to the purchase price for our cheeseburgers and Coke.
If you would like additional problems to help you master this skill, go to our online card catalog at VoxLearn.org, select one of the math collections, and enter the search terms “tax tips commissions”.