If P:Q = 5:4 and P = a+b and Q = a-b, find a:b
Explain how to get the answer
To find the ratio a:b, we need to substitute the values of P and Q into the given equation P:Q = 5:4.
First, let's substitute the values of P and Q:
(a + b) : (a - b) = 5:4
To eliminate the fractions, we can cross-multiply:
4(a + b) = 5(a - b)
Now, distribute the values:
4a + 4b = 5a - 5b
Next, let's gather all the 'a' terms on one side and all the 'b' terms on the other side of the equation:
4b + 5b = 5a - 4a
Combine like terms:
9b = a
To express the ratio a:b, we divide both sides of the equation by 'b':
9b/b = a/b
Simplifying:
9 = a/b
Therefore, the ratio a:b is 9:1.
Alternatively, you can see that a is a multiple of b (a is 9 times b), so the ratio a:b is 9:1.