what formula do I use to solve? a can is filled oil and petrol ratio 1:3 a second can twice size is also filled ratio 2:4 what is the combined ratio?

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to notice that this is proportional problem, hence you need to remember how to solve ratio problems.

You need to remember that you should select one whole to which you need to reffer when you solve the proportional problem.

In this case, the can represents the "whole". You should come up with the notation x for the can, hence, if you need to express the amounts of oil and petrol in the first can, you need to notice that the can is filled up with 4 parts of oil and petrol such that:

First can = 1 part oil + 3 parts petrol = 4 parts oil+petrol

Hence, using fractions to describe the relation above yields:

`x/4 + 3x/4 = 4x/4 = x`

You need to notice that the second can is twice the first can, hence you should use the notation 2x. 

Evaluating the total amount of petrol and oil in the second can yields:

Second can = 2 part oil + 4 parts petrol = 6 parts petrol + oil

`2x*2/6 + 2x*4/6 = 2x`

You need to evaluate how much oil fills up both cans such that:

Total amount of oil = `x/4 + 4x/6 = (3x + 8x)/12 = 11x/12`

You need to evaluate how petrol fills up both cans such that:

Total amount of petrol = `3x/4 + 8x/6 = (9x + 16x)/12 = 25x/12`

Hence, evaluating the combined ratio of total amount of oil and total amount of petrol that fill up both cans yields 11:25.

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najm1947's profile pic

najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

Let a be the quantity filled in first can

Oil = a*1/(1+3) = a/4

Petrol = a*3/(1+3) = 3a/4

Quantity filled in second can = 2a

Oil in second can = 2a*2/(2+4) = 2a/3

Petrol in second can = 2a*4/(2+4) = 4a/3

Total quantity of Oil = a/4+2a/3 = 11a/12

Total quanty of Petrol = 3a/4+4a/3 = 25a/12

Ratio of oil to Petrol = 11a/12 : 25a/12 = 11:25

Combined ratio of Oil and Petrol is 11:25

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