# Homework Help: Solving Ratios in Mathematics?

Asked by shnaz (7) January 6th, 2014

I’m trying to solve this ratio problem. Can’t seem to get around in solving it.

750g of salt is to be divided between three storage cans A,B and C in the ratios A:B = 5:2 and B:C = 3:2. What mass of salt will be stored in each can?

A quick solution would be much appreciated.

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The first step is to combine the two ratios A:B and B:C into one ratio A:B:C.

A:B = 5:2 = 15:6
B:C = 3:2 = 6:4
A:B:C = 15:6:4

Now, this means that if you had 25 grams of salt, then 15g would be in can A, 6g in B, and 4g in C.

You have 750 = 25*30 grams of salt, so these numbers must also be multiplied by 30.

450g in A
180g in B
120g in C

PhiNotPi (12644)

@PhiNotPi‘s solution is quicker, but this is probably what schools teach. If you took Pre-Algebra, you might have run into a problem-solving method called substitution. Important parts in bold.

Describe the problem: 750 = A + B + C (it comes out and tells you this)

You got two ratios, so cross-multiple them (this looks nicer written out). B is in both ratios, so let’s solve each ratio for B. All you need to do is cross-multiply:

First ratio:
A/B=5/2
2A=5B
A = 2.5B
basically, we’re saying A is 2.5 times bigger than B

Second Ratio:
B/C = 3/2
2B=3C
C = ⅔B
that’s a 2 divided by 3, in case your font is tiny – we’re saying C is two-thirds the size of B

Using this information in bold, we can substitute A and C in a way that is described in terms of B and use basic algebra to find the value of B:
750 = A + B +C
750 = 2.5B + B + ⅔B
750=(25/6)B
B = 180
this is how much salt is in container B

Then you can pretty easily solve those two cross multiplied problems in bold from before:
A = 2.5B = 2.5(180) = 450

C = ⅔B = ⅔(180) = 120

And we already figured out B = 180

bolwerk (10305)

Without seeing @PhiNotPi ‘s neat trick, this is how I would do it.

B = 3/2 C
A = 5/2 B = 5/2×3/2 C = 15/4 C
A + B + C = 750
C + 3/2 C + 15/4 C = 750
25/4 C = 750
C = 4/25×750 = 120 g
B = 3/2 C = 180 g
A = 15/4 C = 450 g

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