SOLUTION: if the numerator of a certain fraction is increased by 2 and the denominator is increased by 1, the resulting fraction equals 1/2. if, however, the numerator is increased by 1 and

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: if the numerator of a certain fraction is increased by 2 and the denominator is increased by 1, the resulting fraction equals 1/2. if, however, the numerator is increased by 1 and      Log On


   

Question 540520: if the numerator of a certain fraction is increased by 2 and the denominator is increased by 1, the resulting fraction equals 1/2. if, however, the numerator is increased by 1 and the denominator is decreased by 2, the resulting fraction equals 3/5. Find the fraction
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the numerator
Let b = the denominator
given:
(1) +%28+a+%2B+2+%29+%2F+%28+b+%2B+1+%29+=+1%2F2+
(2) +%28+a+%2B+1+%29+%2F+%28+b+-+2+%29+=+3%2F5+
----------------------------
Multiply both sides of (1) by +2%2A%28+b+%2B+1+%29+
(1) +2%2A%28+a+%2B+2+%29+=+b+%2B+1+
(1) +2a+%2B+4+=+b+%2B+1+
(1) +2a+-+b+=+-3+
Multiply both sides of (2) by +5%2A%28+b+-+2+%29+
(2) +5%2A%28+a+%2B+1+%29+=+3%2A%28+b+-+2+%29+
(2) +5a+%2B+5+=+3b+-+6+
(2) +5a+-+3b+=+-11+
--------------------
Multiply both sides of (1) by 3 and
subtract (1) from (2)
(1) +6a+-+3b+=+-9+
--------------------
(2) +5a+-+3b+=+-11+
(1) +-6a+%2B+3b+=+9+
+-a+=+-2+
+a+=+2+
and, since
(1) +2a+-+b+=+-3+
(1) +2%2A2+-+b+=+-3+
(1) +-b+=+-7+
(1) +b+=+7+
the fraction is a%2Fb+=+2%2F7+
check answer:
(1) +%28+2+%2B+2+%29+%2F+%28+7+%2B+1+%29+=+1%2F2+
(1) +4%2F8+=+1%2F2+
(1) +1%2F2+=+1%2F2+
OK
(2) +%28+2+%2B+1+%29+%2F+%28+7+-+2+%29+=+3%2F5+
(2) +3%2F5+=+3%2F5+
OK