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# The ratio of a to b is 2 to 5 and the ratio of b to c is 3 to 4, what is the ratio of a to c

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To solve this, you need to multiply the ratios together.
(2/5)*(3/4) = A/C
So (2*3)/(5*4) = A/C
6/20 = A/C
You can reduce that be dividing both sides by 2
3/10 = A/C

Here is an example:
Let X = 3
The problem states that A/B = 2/5
So let A = 2X & B = 5X
A = 2*(3) = 6
B = 5*(3) = 15
Now check the ratio: 6/15 = 2/5. The same as what was given.
Now lets look at the ratio for B/C. The given ratio for B/C was 3/4
Using the value of B that we just solved we get:
B = 15
C = (4/3)*15 = 20
Check the ratio.
15/20 = 3/4
Now we have the values for each of the variables
A = 6
B = 15
C = 20
The ratio of A/C is 6/20
6/20 can be reduced to 3/10 be dividing both numbers by 2

Posted on Mar 02, 2011

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