Translate and solve using proportions: 7.25% of what number is $43.64?

Question

Piosellisf · Accepted Answer

Given:  The percent equation &quot;7.25% of what number is $4.64?&quot; to a proportion  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 ab=cd  b. Using colon for a:b=c:d  If an equation in the form of ab=cd is a proportion, then their cross product are equal.  That is, we have  a×c=b×d  Calculation:  Given the below percent equation &quot;7.25% of what number is $4.64?&quot;  We need to first identify the parts of the percent proportion.  In the given percent equation,  $4.64-amount  7.25%-Percent  what number - Base  The above percent equation can be restated as  &quot;$4.64 out of what number is the same as 7.25 out of 100&quot;  Let us assume that the number is x  Thus, the proportion is given as  4.64x=7.25100  Now, let us solve the above proportion.  We know that, the cross product is equal.  Thus, we have  4.64×100=7.25×x  7.25×x=4.64×100  x=4.64×1007.25  x=4647.25  x=64  Conclusion:  Hence, the proportion is 4.64x=7.25100  On solving the proportion, the number is 64.

Robert Pina · Accepted Answer

Step 1
Solution by Cross Multiplication
For the equation

\frac{4.64}{x} = \frac{7.25}{100}

The cross product is

4.64 \times 100 = x \times 7.25

Solving for x

x = \frac{4.64 \times 100}{7.25}

and reducing

x = 64

Solution by Proportion
Since the equation is an equality
If

7.25 \div 4.64 = 1.5625

Then it is true that

100 \div x = 1.5625

Solvinf for x

x = 100 \div 1.5625

x = 64

Translate and solve using proportions: 7.25% of what number is

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