In a problem on percentages there are three quantities that are involved. These are the base, the amount, and the rate percent. Express the relation between them in the form of an equation and explain with examples how to find each one of them given the other two quantities.
In problems related to percentages, there are primarily three quantities involved: the base, the amount, and the rate percent. The base represents the whole or the original quantity, the amount represents the part or the portion of the base, and the rate percent represents the percentage value.
To express the relation between them in the form of an equation, we can use the formula:
Amount = (Rate percent/100) x Base
Now let's discuss how to find each one of these quantities, given the other two.
1. To find the amount:
Given the base and the rate percent, you can use the formula above to calculate the amount. You multiply the rate percent by the base and divide by 100.
For example, let's say the base is 400 and the rate percent is 25%. To find the amount, you can use the equation:
Amount = (25/100) x 400 = 100
2. To find the base:
Given the amount and the rate percent, you can rearrange the formula to solve for the base. Divide the amount by the rate percent divided by 100.
For example, let's say the amount is 75 and the rate percent is 15%. To find the base, you can rearrange the formula as follows:
Base = Amount / (Rate percent/100) = 75 / (15/100) = 500
3. To find the rate percent:
Given the base and the amount, rearrange the formula and solve for the rate percent. Divide the amount by the base, then multiply by 100.
For example, let's say the base is 600 and the amount is 200. To find the rate percent, you can rearrange the formula as follows:
Rate percent = (Amount / Base) x 100 = (200 / 600) x 100 = 33.33%
By using the equation and the given values, you can calculate any of the three quantities: base, amount, or rate percent, depending on what is given in the problem.
The relation between the base, the amount, and the rate percent can be expressed using the following equation:
Amount = Base + (Rate Percent/100) * Base
To find each quantity, given the other two, follow the steps below:
1. Finding the Amount:
To find the amount, given the base and the rate percent, use the formula mentioned above. Let's consider an example:
Example 1:
Base = $1000
Rate Percent = 20%
Amount = Base + (Rate Percent/100) * Base
= $1000 + (20/100) * $1000
= $1000 + $200
= $1200
Therefore, the amount in this example is $1200.
2. Finding the Base:
To find the base, given the amount and the rate percent, rearrange the equation as follows:
Base = Amount / (1 + (Rate Percent/100))
Example 2:
Amount = $1500
Rate Percent = 15%
Base = Amount / (1 + (Rate Percent/100))
= $1500 / (1 + (15/100))
= $1500 / (1 + 0.15)
= $1500 / 1.15
≈ $1304.35
Therefore, the base in this example is approximately $1304.35.
3. Finding the Rate Percent:
To find the rate percent, given the base and the amount, rearrange the equation as follows:
Rate Percent = ((Amount - Base) / Base) * 100
Example 3:
Base = $2000
Amount = $2400
Rate Percent = ((Amount - Base) / Base) * 100
= (($2400 - $2000) / $2000) * 100
= ($400 / $2000) * 100
= 0.2 * 100
= 20%
Therefore, the rate percent in this example is 20%.
By using these equations and examples, you can find the base, amount, and rate percent given any two of the quantities.