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HELLO ,

1.WHEN 1 IS ADDED TO THE NUMERATOR OF A FRACTION, THE FRACTION BECOMES 1 BY 2, BUT WHEN 3 IS ADDED TO ITS DENOMINATOR IT BECOMES 1 BY 3 . FIND THE FRACTION .

2.IF 2 IS ADDED TO THE NUMERATOR OF A FRACTION AND 1 IS SUBTRACTED FROM ITS DENOMINATOR , THE FRACTION BECOMES 4 BY 5 .IF 1 IS ADDED TO THE DENOMINATOR OF THE FRACTION , THE FRACTION BECOMES 1 BY 2 . FIND THE FRACTION.

3.THE SUM OF THE DIGITS IN A 2- DIGIT NO. IS 7 .

IF 9 IS SUBTRACTED FROM THE NO. ,ITS DIGTS ARE REVERSED . FIND THE NO.

4.THE DIGIT IN THE TENS PLACE OF A 2- DIGIT NO. IS HALF THE DIGIT IN THE ONES PLACE . IF THE SUM OF THE DIGITS IS 12 , FIND THE NO.

5.A 2-DIGIT NO. OS 5 TIMES THE SUM OF ITS DIGITS. IF 9 IS ADDED TO THE NO. , ITS DIGITS ARE REVERSED . FIND THE NO.

6.A 2-DIGIT NO. IS 3 TIMES THE THE SUM OF ITS DIGITS. IF 45 IS ADDED TO THE NO. ,ITS DIGITS ARE REVERSED . FIND THE NO.

Hello Astina,

Since you have so many questions here, I will just give the equations and

solutions...leaving to you the algebra.

1. Let x/y be the fraction. Thus, (x+1)/y=1/2 AND x/(y+3)=1/3

...solving gives x=5, y=12 ==> x/y=5/12

2. Let x/y be the fraction. Thus, (x+2)/(y-1)=4/5 AND x/(y+1)=1/2

...solving gives x=6, y=11 ==> x/y=6/11

3. Let 10x+y be the two-digit number ("xy"). Thus, x+y=7 AND (10x+y)-9=10y+x

...solving gives: x=4, y=3...so the number is 43.

4. Let 10x+y be the two-digit number ("xy"). Thus, x=y/2 AND x+y=12

...solving gives: x=4, y=8...so the number is 48.

5. Let 10x+y be the two-digit number ("xy"). Thus, 10x+y=5(x+y) AND 10x+y+9=10y+x

...solving gives: x=4, y=5...so the number is 45

6. Let 10x+y be the two-digit number ("xy"). Thus, 10x+y=3(x+y) AND 10x+y+45=10y+x

...solving gives: x=2, y=7...so the number is 27

Abe

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Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

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M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook