SOLUTION: If the numerator and denominator of a fraction are both decreased by three, the fraction becomes 4\5. If the numerator and denominator are both increased by three, the fraction bec

Question 132927: If the numerator and denominator of a fraction are both decreased by three, the fraction becomes 4\5. If the numerator and denominator are both increased by three, the fraction becomes 7\8.
1. Write down two equations from the statement?
2. Solve the equations simultaneously to get the original fraction.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=numerator of original fraction
And let y=denominator of original fraction
We are told that:
(x-3)/(y-3)=4/5 multiply each side by 5(y-3)
5(x-3)=4(y-3) get rid of parens
5x-15=4y-12 subtract 4y from and add 15 to both sides
5x-15+15-4y=4y-4y-12+15 collect like terms
5x-4y=3---------------------------------------------eq1
We are also told that:
(x+3)/(y+3)=7/8 multiply each side by 8(y+3)
8(x+3)=7(y+3) get rid of parens
8x+24=7y+21 subtract 7y and also 24 from both sides
8x-7y+24-24=7y-7y+21-24 collect like terms
8x-7y=-3------------------------------------------eq2
Multiply each term in eq1 by 8
40x-32y=24-----------------------------------eq1a
Multiply each term in eq2 by 5
40x-35y=-15-------------------------------------eq2a
subtract eq1a from eq2a
-3y=-39 divide both sides by -3
y=13--------------------------------------denominator of original fraction

Substitute y=13 into eq1
5x-4*13=3
5x-52=3 add 52 to both sides
5x-52+52=3+52 collect like terms
5x=55 divide both sides by 5
x=11-------------------------------------numerator of original fraction
CK
(11-3)/(13-3)=4/5
8/10=4/5
4/5=4/5
also
(11+3)/(13+3)=7/8
14/16=7/8
7/8=7/8

Hope this helps----ptaylor
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