Question

a teacher had 21 red pens. if the ratio of red pens to blue pens she owned was 3:1 , how many pens did she have in total

Answer 1

She had 21:7 because if you multiply 3:1 by 7 each it is 21:7 so she had 7 blue pens

Answer 2

There are 21 red pens. For every 3 red pens, there is 1 blue pen.
Let's make these into a fraction equation.
21/p=3/1
p is the number of blue pens we have yet to find.
First, cross multiply.
21x1=21
px3=3p
Now, we have an equation of
21÷3p
We set it equal to 1, and we solve it.
21÷3p = 1
(21÷3p)×3p=1×3p
21=3p
21÷3=(3p)÷3
7=p
So, if there are 21 red pens, there are 7 blue pens.
We add these together to find the total number of pens the teacher has.
21+7=28
The teacher has 28 pens total.