# Homework Help: Solving Ratios in Mathematics?

Asked by

shnaz (

7
)
3 months ago

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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## 4 Answers

Response moderated (Unhelpful)

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‘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

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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