### Instruction: In a jumbo bag of bows, $\frac{1}{5}$ are red, $\frac{1}{2}$ are blue, $\frac{1}{10}$ are green and the remaining 30 are white. How many of the bows are green?### Response: Let's call the total number of bows x.
So then the number of red bows is $\frac{1}{5}x$.
And the number of blue bows is $\frac{1}{2}x$.
And the number of green bows is $\frac{1}{10}x$.
And the number of white bows is 30.
So we can write an equation that says x equals the sum of the number of each type of bow.
Right. So $x=\frac{1}{5}x+\frac{1}{2}x+\frac{1}{10}x+30$.
Now we can just solve for x.
First we should simplify the equation. So $\frac{1}{5}x+\frac{1}{2}x+\frac{1}{10}x=\frac{1}{5}x+\frac{5}{10}x+\frac{1}{10}x=\frac{6}{10}x+\frac{1}{10}x=\frac{7}{10}x$.
So our new equation is $x=\frac{7}{10}x+30$.
If we subtract $\frac{7}{10}x$ from both sides we get $\frac{3}{10}x=30$.
And if we divide both sides by $\frac{3}{10}$ we get $x=100$.
So there are 100 total bows.
If $\frac{1}{10}$ of the bows are green then the number of green bows is $\frac{1}{10}*100=10$.