Solve the word problem.

Question

An integer is 4 less than another integer. If the reciprocal of the larger integer is added to thrice the reciprocal of the smaller integer, the sum is 5/3. What are the two integers?

Answer 1

S=L-4

1/L +3/S = 5/3

1/L +3/(L-4) = 5/3

multiply by 3L(L-4) to get

3L-12 + 9L = 5L^2 -20L

5L^2 -32L +12 = 0

(5L-2)(L-6) = 0

L=6, 2/5

S=6-4 =2

the numbers are 2 and 6

1/6 + 3/2 = 5/3