Question

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

Ratios, rates, proportions
ANSWERED
asked 2021-08-09
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.
40
 
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