One number is three times another. The sum of their reciprocals is 4. What are the two numbers?

Answer 1

This is a two equation problem. Since one numbner is three times the other, the first equation is y = 3x. Next the reciprocals of the two numbers add up to four, so 1/x + 1/y = 4.

The first equation gives y in terms of x, so substitute 3x for y in the second equation

1/x + 1/3x = 4.

You can't add the x terms yet because the denominators are not the same. Change that by multiplying the top and bottom of 1/x by 3. That gives 3/3x, and is equivalent to 1/x, so put 3/3x into the second equation instead of 1/x.

3/3x + 1/3x = 4, add terms

4/3x = 4, multiply both sides by 3x

4 = (4 x 3x) = 12x, then divide both sides by 4

1 = 3x, solve for x

1/3 = x

Now solve for y using y = 3x, so y = 1

Check by put y = 1 and x = 1/3 into the original equations

y = 3x,

1 = 3(1/3). Check

1/x + 1/y = 4

(1/(1/3) + 1/1 = 4

3 + 1 = 4. Check

Hope this helps