Calculate two variables with knowledge of the sum of (a+b) and the ratio of (a/b)

Question

I know what I want the sum of two variables (a and b) to be and I know what the ratio of a to b should be. How can I set up a formula to calculate the values of each variable given the known sum and ratio? The ratio of a/b should ALWAYS equal 0.6900. So if a=0.4083 then b=0.5917. In this example, a+b=1.0000. So for example, how can I calculate the values for a and b if I know that a+b=2.000 and that a/b=0.6900? (hint: I know that the answer should be a=0.8166 and b=1.1834 but I don't know how to calculate that automatically without plug and chug)

Answer 1

We know that a + b =2 and a/b = .69

We then also know that a = .69 b (just multiply both sides by b)

 

Then we substitute .69b for a in the first equation giving us:

 

.69 b + b = 2

adding up the b's gives us

 

1.69 b =2 

 

dividing both sides by 1.69 gives us

 

b = 2/1.69 or 1.1834 and 

a = 2 - 1.1834

a= .8166

 

Hope this helps