# How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths many sailors as soldiers?

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There are 4/5 as many sailors as soldiers. Let the number of sailors be denoted by Sa and the number of soldiers be denoted by Sd.

So we have Sa = (4/5)*Sd.

Also Sa + Sd = 27

=> (4/5)Sd + Sd = 27

=> (4/5)Sd + (5/5)*Sd = 27

=> (4/5 + 5/5)Sd = 27

=> (9/5)*Sd = 27

=> Sd = 27*(5/9)

=> Sd = 3*5

=> Sd = 15

**Therefore there are 15 soldiers in the group.**

Let the number of sailors be x and the number of soldiers be y.

Then, given that there are 4/5 sailors as many as soldiers.

==> y = (4/5) x.

But, given that all together are 27.

==> x + y = 27.

Let us substitute with y= (4/5)x

==> x + (4/5)x = 27

==> (9/5)x = 27

==> x = 27*5/9 = 3*5 = 15

**Then, there are 15 sailors.**

==> y= (4/5)x = (4/5)*15 = 12

**Then, there are 12 soldiers.**

Given that there are four fifths as many sailors as soldiers.

That is, if there x soldiers in the group, then then there are 4x/5 sailors. Together they are x+4/x = 9x/5 in the group.

But actually there are 27 soldiers in the group.

=> 9x/5 = 27.

We multiply both sides by 5/9 and get:

Therefore (9x/5)*(5/9) = 27*(5/9) = 15.

x = 15.

Therefore the number of soldiers = x = 15.

The number of sailors = 4x/5 = (4/5)15 =12.

Seems we have two different answers here.

The numbers are 12 and 15.

According to the Canadian forces practice test the answer is 15 soldiers.

I am still looking for the right answer.