What proportion can be used to find 65% of 90?
What proportion can be used to find 65% of 90?
The Correct Answer and Explanation is:
Correct Answer:
To find 65% of 90 using a proportion, you can set it up like this: 65100=x90\frac{65}{100} = \frac{x}{90}
This proportion means: 65 is to 100 as x is to 90, where x represents 65% of 90.
Explanation:
A proportion is a statement that two ratios or fractions are equal. In the context of percentages, a proportion can help us find the part of a whole that corresponds to a certain percent.
In this case, we want to find 65% of 90. The percent symbol (%) means “per hundred,” so 65% is the same as the fraction 65100\frac{65}{100}.
To find what 65% of 90 is, we are essentially asking: What number (x) is to 90 what 65 is to 100? This is a classic proportion problem. The proportion: 65100=x90\frac{65}{100} = \frac{x}{90}
says that the ratio of 65 to 100 should equal the ratio of some number x to 90. Solving this proportion will give us the value of x, which is 65% of 90.
To solve the proportion, you use cross-multiplication: 65×90=100×x65 \times 90 = 100 \times x 5850=100×5850 = 100x x=5850100=58.5x = \frac{5850}{100} = 58.5
So, 65% of 90 is 58.5.
Using proportions to solve percent problems is helpful because it applies a consistent, logical method to convert between percentages, decimals, and actual values. This technique is especially useful for students who are learning algebra and need a structured way to set up and solve word problems. It also visually demonstrates the relationship between parts and wholes in a way that builds understanding for more complex math topics in the future.
