Question # Translate and solve using proportions: 85\% of what number is

Ratios, rates, proportions
ANSWERED Translate and solve using proportions: $$\displaystyle{85}\%$$ of what number is $3.23? ## Expert Answers (1) 2021-08-10 Formula used: Proportion is referred to as a statement that says two ratios are equal. There are two ways to write a proportion: a. Using fraction form $$\displaystyle{\frac{{{a}}}{{{b}}}}={\frac{{{c}}}{{{d}}}}$$ b. Using colon for $$\displaystyle{a}:{b}={c}:{d}$$ If an equation in the form of $$\displaystyle{\frac{{{a}}}{{{b}}}}={\frac{{{c}}}{{{d}}}}$$ is a proportion, then their cross product are equal. That is, we have $$\displaystyle{a}\times{c}={b}\times{d}$$ Calculation: Given the below percent equation "$$\displaystyle{8.5}\%$$ of what number is$3.23?"
We need to first identify the parts of the percent proportion.
In the given percent equation,
\$3.23-amount
$$\displaystyle{8.5}\%$$-Percent
what number - Base
The above percent equation can be restated as
"3.23 out of what number is the same as 8.5 out of 100"
Let us assume that the number is x
Thus, the proportion is given as
$$\displaystyle{\frac{{{3.23}}}{{{x}}}}={\frac{{{8.5}}}{{{100}}}}$$
Now, let us solve the above proportion.
We know that, the cross product is equal.
Thus, we have
$$\displaystyle{3.23}\times{100}={8.5}\times{x}$$
$$\displaystyle{8.5}\times{x}={3.23}\times{100}$$
$$\displaystyle{x}={\frac{{{3.23}\times{100}}}{{{8.5}}}}$$
$$\displaystyle{x}={\frac{{{323}}}{{{8.5}}}}$$
$$\displaystyle{x}={38}$$
Conclusion:
Hence, the proportion is $$\displaystyle{\frac{{{3.23}}}{{{x}}}}={\frac{{{8.5}}}{{{100}}}}$$
On solving the proportion, the number is 38.