One month a business earns 40,000 in revenue. The next...

One month a business earns $\$ 40,000$ in revenue. The next month the business increases the revenue55000. a. Is $\$ 40,000$ an initial amount, a final amount, or an increase amount? b. Is $\$ 5000$ an initial amount, a final amount, or an increase amount? c. With the information given, to find the percent of increase, do you need to subtract prior to setting up the proportion? Why or why not? d. Write a proportion that can be used to find the percent of increase. Jana notes that her July electricity bill is $\$ 8.96$ higher than last year's amount. If last year's bill was $\$ 148.75,$ what is the percent of increase?

One month a business earns $\$ 40,000$ in revenue. The next month the business increases the revenue55000.
a. Is $\$ 40,000$ an initial amount, a final amount, or an increase amount?
b. Is $\$ 5000$ an initial amount, a final amount, or an increase amount?
c. With the information given, to find the percent of increase, do you need to subtract prior to setting up the proportion? Why or why not?
d. Write a proportion that can be used to find the percent of increase.
Jana notes that her July electricity bill is $\$ 8.96$ higher than last year's amount. If last year's bill was $\$ 148.75,$ what is the percent of increase?

Key Concepts

Proportional Reasoning in Percentage Calculations

Establishing a proportion in percentage calculations involves setting up a ratio that equates the increase amount to a percentage of the initial amount. This approach is useful because it directly relates the part to the whole, making it straightforward to solve for an unknown percentage using basic algebra.

Initial Amount

The initial amount is the starting value before any change occurs. It serves as the base figure used to determine the relative size of any subsequent increases or decreases. In percentage change calculations, it is the denominator against which change is measured.

Final Amount

The final amount is the value after the change has taken effect. It is the result obtained after adding or subtracting the increase or decrease to the initial amount. In percent increase problems, it helps to determine the total change from the starting point.

Increase Amount

The increase amount is the difference between the final amount and the initial amount. It represents the actual change that has occurred and is used to compute relative change by comparison with the initial amount.

Percent Increase

Percent increase quantifies how much a quantity has grown in relation to its original size, expressed in percent. It is calculated by dividing the increase amount by the initial amount and then multiplying by 100, allowing for easy comparison of growth regardless of the absolute numbers.

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