Solving Multi-step Percentage Problems
Student Summary
To find a 30% increase over 50, we can find 130% of 50.
1.3⋅50=65
To find a 30% decrease from 50, we can find 70% of 50.
0.7⋅50=35
If we know the initial amount and the final amount, we can also find the percent increase or percent decrease. For example, a plant was 12 inches tall and grew to be 15 inches tall. What percent increase is this? Here are two ways to solve this problem:
The plant grew 3 inches, because 15−12=3. We can divide this growth by the original height: 3÷12=0.25. So the height of the plant increased by 25%.
The plant’s new height is 125% of the original height, because 15÷12=1.25. This means the height increased by 25%, because 125−100=25.
Consider this new example: A rope was 2.4 meters long. Someone cut it down to 1.9 meters. What percent decrease is this? Here are two ways to solve the problem:
The rope is now 2.4−1.9, or 0.5, meter shorter. We can divide this decrease by the original length: 0.5÷2.4=0.2083. So the length of the rope decreased by approximately 20.8%.
The rope’s new length is about 79.2% of the original length, because 1.9÷2.4=0.7916. The length decreased by approximately 20.8%, because 100−79.2=20.8.
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