Calculating The Amount Of Increase
Calculating The Amount Of Increase is a Grade 8 math skill in Saxon Math Course 3, Chapter 7, where students find the actual numerical increase when a quantity changes by a given percent, using the formula: amount of increase = percent times original amount. This skill is applied to contexts like markups, salary raises, price increases, and population growth.
Key Concepts
Property To find the specific amount of change from an increase, use a proportion comparing the percent increase to the new total percent (100% + increase %). $$ \frac{\text{Increase \%}}{100 + \text{Increase \%}} = \frac{\text{Amount of Change}}{\text{New Value}} $$.
Examples A collectible's value rose 10% in one year to 550 dollars. By how many dollars did its value increase? $$\frac{10}{110} = \frac{c}{550} \rightarrow 110c = 5500 \rightarrow c = 50$$. The value increased by 50 dollars. A town's population grew by 30% to 13,000 people. How many new people moved to the town? $$\frac{30}{130} = \frac{c}{13000} \rightarrow 130c = 390000 \rightarrow c = 3000$$. The population increased by 3000 people.
Explanation When a value goes up, the new amount is more than 100% of the original. If a price rises by 20%, the new price is 120% of the old one. We can then set up a proportion comparing the percent increase to the total new percent, which allows us to find the exact dollar amount of that increase.
Common Questions
How do you calculate the amount of increase?
Multiply the original amount by the percent increase (as a decimal). Amount of increase = percent rate times original amount. For example, a 15 percent increase on 200 is 0.15 times 200 = 30.
What is the difference between the amount of increase and the new total?
The amount of increase is just the added portion. The new total is the original amount plus the amount of increase.
How do you find the new total after a percent increase?
Add the amount of increase to the original amount, or multiply the original by (1 + percent as decimal). For example, 200 increased by 15 percent: 200 + 30 = 230, or 200 times 1.15 = 230.
What are real-world examples of calculating amount of increase?
Calculating a salary raise in dollars, finding the markup amount on a wholesale item, computing interest earned, and determining population growth all use this method.
Where is calculating amount of increase taught in Grade 8?
This skill is covered in Saxon Math Course 3, Chapter 7: Algebra.