After the number-thief stole five-sevenths of this number, only 30 was left. What was the number?
+895 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.
+895 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.
