Separate 35 into two parts such that 4 times the larger is 4 less than five times the smaller

Name: Barbara
Who is asking: Student
Level of the question: Secondary

Question: Separate 35 into two parts such that 4 times the larger is 4 less than five times the smaller.

Hi Barbara.

You have to find two numbers, but there is a relation between them. In algebra like this, we try to reduce the problem to just one unknown number.

Let L = larger number and S = smaller number

L + S = 35

and

4L = 5S - 4

If you re-write these, solving for L each time, you get

L = 35 - S

and

L = (5S - 4 ) / 4

These are the same S and L we're talking about, so that means that

35 - S = (5S - 4) / 4

Now you just have to solve for S and then use that value in the equation L = 35 - S to get the other number.

Hope this helps!
Stephen La Rocque>