ch 6.6-6.7 homework

Question

One number is 8 times another. The sum of their reciprocals is 27/8. Find the numbers.

 

smaller value=?

 

larger value=?

Answer 1

One number is 8 times another.

x = 8y

 

The sum of their reciprocals is 27/8.

1/x + 1/y = 27/8

 

We can substitute 8y in place of x in the 2nd equation

in order to solve for y

 

1/8y + 1/y = 27/8

 

1/8y + 8/8y = 27/8

 

9/8y = 27/8

 

Cross multiply

27(8y) = 9(8)

216y = 72

y = 72/216

y = 1/3

 

x = 8y = 8(1/3) = 8/3

 

Your numbers are 8/3 and 1/3

 

Check:

1/x + 1/y = 27/8

 

1/(8/3) + 1/(1/3) = 27/8

3/8 + 3 = 27/8

3/8 + 24/8 = 27/8

27/8 = 27/8

Equation balances and answer is correct.