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

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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

#1
+681
+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.

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#1
+681
+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.

#2
+5922
+1

That is a really good way to explain it!!

hectictar  Sep 30, 2017
#3
+681
+1

Thanks!