SOLUTION: one interger is 2 less than another integer.3 times the reciprocal of the lesser interger plus five times the reciprocal of the greater is 7/8. What are the two integer?

Question 401812: one interger is 2 less than another integer.3 times the reciprocal of the lesser interger plus five times the reciprocal of the greater is 7/8. What are the two integer?
Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
x-2=y can be used IF x is the largest integer,
x+2=y is used when x is the smaller integer.
X+2=Y
3*1/X+5*1/Y=7/8
3/X+5/Y=7/8
3/X+5/(X+2)=7/8
[3(X+2)+5X]/X(X+2)=7/8
[3X+6+5X]/(X^2+2X)=7/8 CROSS MULTIPLY.
7(X^2+2X)=8(8X+6)
7X^2+14X=64X+48
7X^2+14X-64X-48=0
7X^2-50X-48=0
(7X+6)(X-8)=0
X-8=0
X=8 ANS. FOR THE SMALLER INTEGER.
8+2=10 ANS. FOR THE LARGER INTEGER.
PROOF:
3/8+5*1/10=7/8
3/8+5/10=7/8
3/8+1/2=7/8
3/8+4/8=7/8
7/8=7/8

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