SOLUTION: Find two consecutive integers such that the sum of one-half the first and three-fifths the second is 27

Question 658818: Find two consecutive integers such that the sum of one-half the first and three-fifths the second is 27
Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
LET X BE THE FIRST INTEGER.
LET (X+1) BE THE SECOND INTEGER.
X/2+3/5(X+1)=27
X/2+3(X+1)/5=27
X/2+(3X+3)/5=27 FIND A COMMON DENOMINATOR FOR THE 2 FRACTIONS.
2 4 6 8 (10) 12 14
5 (10) 15 20
2*5=10 IS THE LOWEST COMMON DENOMINATOR
[5X+2*(3X+3)]/10=27
[5X+6X+6]/10=27 CROSS MULTIPLY.
11X+6=270
11X=270-6
11X=264
X=264/11
X=24 ANS. FOR THE FIRST INTEGER.
24+1=25 ANS. FOR THE SECOND INTEGER.
PROOF:
24/2+3/5*25=27
12+75/5=27
12+15=27
27=27
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