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# If I have 18 red pens. What's the ratio of red to blue if I have 3:5?

I have 18 red pens . If the ratio of red to blue pens is 3 to 5; how many do I have?

### 4 Answers by Expert Tutors

Johnny R. | Exceptional Math and Accounting TutorExceptional Math and Accounting Tutor
4.8 4.8 (162 lesson ratings) (162)
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Juliet,

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.

4.9 4.9 (233 lesson ratings) (233)
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Hey Julliet -- 18 reds means having 6 sets of 3 ... also need 6 sets of 5 blues or 30 more ... 48 total :)

Fatima K. | Seasoned to perfection... let's study together!Seasoned to perfection... let's study to...
4.8 4.8 (115 lesson ratings) (115)
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ratio is 3:5 so the sum of ratio is 8.

since we do no know the total number of pens so we can assume it to be 'x'

now you can solve by 3/8 of 'x' = 18    (18 is the total number of red pens)

3/8*x = 18

x = 48 (total number of pens)

red pens = 18  blue pens = 30         (blue pens: 5/8*48 = 30)

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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red/(red+blue) = 3/(3+5) = 3/8 = 3*6/(8*6) = 18/48

So, you have 48 pens: 18 red pens and 30 blue pens.