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Solve each equation mentally.
For each situation:
The water level in a reservoir is now 52 meters. If this was a 32% increase, what was the initial depth?
Diagram:
Equation:
Solution:
The snow is now 52 inches deep. If this was a 68% decrease, what was the initial depth?
Diagram:
Equation:
Solution:
Write an equation to represent each situation. Then, solve the equation.
A piece of fabric weighed 15 ounces. After it was decorated with zardozi, the weight had increased by 82%. What is the weight of the finished piece?
Before making a mola, the layers of fabric weighed 4.7 ounces. When the mola was finished, the weight had decreased by 17%. What is the weight of the finished mola?
Another finished mola weighs 4.9 ounces. This is a 21% decrease from the original weight of the fabric. What was the original weight?
Last year, scientists counted 12 foxes in a conservation area. This year, they counted 50% more than that. How many foxes did they count this year?
Explain why this situation can be represented by the equation . Make sure that you explain what represents.
We can use equations to express percent increase and percent decrease.
For example, if is 15% more than , we can represent this by using any of these equations:
So if someone makes an investment of dollars, and its value increases by 15% to reach \$1,250, then we can write the equation to find the value of the initial investment.
Here is another example: if is 7% less than , we can represent this by using any of these equations:
So if the amount of water in a tank decreased 7% from its starting value of to its ending value of 348 gallons, then we can write .
Often, an equation is the most efficient way to solve a problem involving percent increase or percent decrease.