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After the number-thief stole five-sevenths of this number, only 30 was left. What was the number?

Guest Sep 30, 2017

Best Answer 

 #1
avatar+771 
+2

Let's say x is the mystery number.

So first you have x.

Then you take away 5/7 of x.

\(x-\frac{5}{7}x\)

That equals 30.

\(x-\frac{5}{7}x=30\)

This is the same as 2/7x equals 30.

\(\frac{2}{7}x=30\)

You divide both sides by 2/7.

\(x=\frac{30}{\frac{2}{7}}\)

But when you divide by a fraction, it is the same as multiplying by the reciprocal.

\(x=30*\frac{7}{2}\)

Simplify.

\(x=\frac{30*7}{2}\)

\(x=\frac{210}{2}\)

\(x=105\)

A good way to test this is by plugging it into the original equation.

\(x-\frac{5}{7}x=30\)

Substitute each x for 105.

\(105-\frac{5}{7}(105)=30\)

\(105-\frac{525}{7}=30\)

\(105-75=30\)

\(30=30\)

This is true, so your mystery number is 105.

AdamTaurus  Sep 30, 2017
 #1
avatar+771 
+2
Best Answer

Let's say x is the mystery number.

So first you have x.

Then you take away 5/7 of x.

\(x-\frac{5}{7}x\)

That equals 30.

\(x-\frac{5}{7}x=30\)

This is the same as 2/7x equals 30.

\(\frac{2}{7}x=30\)

You divide both sides by 2/7.

\(x=\frac{30}{\frac{2}{7}}\)

But when you divide by a fraction, it is the same as multiplying by the reciprocal.

\(x=30*\frac{7}{2}\)

Simplify.

\(x=\frac{30*7}{2}\)

\(x=\frac{210}{2}\)

\(x=105\)

A good way to test this is by plugging it into the original equation.

\(x-\frac{5}{7}x=30\)

Substitute each x for 105.

\(105-\frac{5}{7}(105)=30\)

\(105-\frac{525}{7}=30\)

\(105-75=30\)

\(30=30\)

This is true, so your mystery number is 105.

AdamTaurus  Sep 30, 2017
 #2
avatar+7324 
+1

That is a really good way to explain it!! smiley

hectictar  Sep 30, 2017
 #3
avatar+771 
+1

Thanks!

AdamTaurus  Sep 30, 2017

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