SOLUTION: Find the ratio a:c if a:b= 1:2, b:d = 4:5, d:c = 3:1

Question 208973: Find the ratio a:c if a:b= 1:2, b:d = 4:5, d:c = 3:1
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Find the ratio a:c if a:b= 1:2, b:d = 4:5, d:c = 3:1
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x : y is the same as is the same as x divided by y
see reference: http://www.icoachmath.com/sitemap/Ratio.html
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a:b means which means that and
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b:d means which means that and
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d:c means which means that and
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now that you have these translations out of the way you can solve.
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a:c means
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to find you need to find relationships in terms of a and c and then solve.
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in order to get a relationship from a to c, you need to go through b and d because there is no direct relationship between a and c.
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start with the relationship between a and b.

get the relationship from b to d

replace b with to get:
which becomes:

get the relationship from d to c

replace d with 3c to get:
which becomes:
which becomes:

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is the same as:
which is the same as:

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to confirm, let's try to find c directly and then try to find c indirectly.
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let a = 6
if , then c must equal to = =
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we know that a = 6 and c = 5 solving directly.
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let's find c indirectly.
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we start off with a = 6
we know that = = =
we know that = = =
we know that = = =
we have and solving indirectly.
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the formulas check out and the relationship you are looking for is:

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is there an easier way to do this?
yes there is
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the shortcut method is as follows:
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you have =
you know those ratios are:
and and
you know this is the same as:
and and
so you have:
= = = = =
your ratio for
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