Have you ever enjoyed autumn? Take a look at this dilemma involving trees and their leaves.
By mid-September, 50% of the trees lose their leaves. If 850 trees in a grove lost their leaves, how many trees are there in all?
Use the percent equation to solve this problem. You will learn all that you need to know in this Concept.
Did you know that you can use the percent equation to solve percent problems? Take a look at how you can move from the proportion to the percent equation.
Okay, let’s go through it again. Look at what we just wrote.
We wrote the same thing we just didn’t include values. The variables stayed and we multiplied them.
This situation showed us how to use go from a proportion to the percent equation when solving for part a.
78 is 65% of what number?
Here we know that the word “is” means equals. The numbers may be in a different location, but just pay attention to the key words and you will know what to do. Notice that we have been given the percent and we are missing the “of what number” that is the value of the base. Let’s write the equation.
To work with the 65%, it makes sense to convert it to a decimal. We do this by dropping the percent sign and moving the decimal two places to the left.
This is the answer.
Here is another one.
11 is 77% of what number?
Once again, pay attention to the key words. You can see that we are once again going to be looking for the value of the base. Let’s write the equation.
Convert the percent to a decimal and solve.
In this problem, you could round to the nearest hundredths place as we did here. Sometimes, you may be asked to round to the nearest tenths place. In that case, the answer would have been 14.3.
Solve each problem using the percent equation.
10 is 50% of what number?
45 is 20% of what number?
68 is 40% of what number?
Now let's go back to the dilemma from the beginning of the Concept.
Let’s start by breaking apart this problem. We have a percent, so we know that we won’t be looking for the percent. We know that 850 trees in a grove lost their leaves, but we don’t know the total number of trees in the grove. The total could be thought of as the whole and this is the base. We are going to be looking for the base.
Let’s write the equation.
Now we solve by dividing both sides of the equation by .50.
There are 1700 trees in the grove.
a part of a whole out of 100.
Here is one for you to try on your own.
25 is 60% of what number?
First, let's write down the percent equation.
In this problem, we are solving for the base. Let's fill in the values that we know.
Solving Percent Problems with the Percent Equation
Directions: Solve each percent problem. You may round your answers to the nearest tenth when necessary.
- 23 is 9% of what number?
- 10 is 35% of what number?
- 580 is 82% of what number?
- 58 is 8% of what number?
- 58 is 80% of what number?
- 11 is 82% of what number?
- 33 is 2% of what number?
- 14 is 9% of what number?
- 50 is 67% of what number?
- 33 is 45% of what number?
- 40 is 80% of what number?
- 68 is 99% of what number?
- 78 is 55% of what number?
- 16 is 12% of what number?
- 1450 is 80% of what number?