I have 18 red pens . If the ratio of red to blue pens is 3 to 5; how many do I have?
For this problem, we are trying to determine the ratio of red pens to blue pens. Therefore we are trying to determine the proportion of red pens to blue pens..
A proportion is an equation which states that two ratios are equal.
Lets identify our proportion
We know that the known proportion or ratio is 3/5.
3 = the ratio of red pens. we have 18 red pens.
5 is the ratio of blue pens. We are trying to determine the number of blue pens we have.
The number of blue pens is our unknown. We will call our unknown x.
Our proportion is 3/5= 18/x
To solve a proportion we cross multiply.
Cross multiplication is the multiplication of the numerator of the first ratio by the denominator of the second ratio and the multiplication of the denominator of the first ratio by the numerator of the second ratio.
3/5 = 18/x
Cross multiply 3(numerator) x x(denominator) = 5(denominator) x 18 (numerator)
This becomes 3x = 90
To solve divide both sides by 3 (using the inverse operation to isolate x)
3x/3 = 90/3
x = 30
We have determined we have 18 red pens and 30 blue pins. We have a total of 48 pins.
Our proportion becomes 3/5 = 18/30
Note: The solutions provided by the other tutors who answered this question are all good solutions. This is an alternative method I provided to expand your knowledge.