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Word Problems/WORD PROMBLEMS ON SIMULTANEOUS LINEAR EQUATIONS

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Question
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.

Answer
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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Abe Mantell

Expertise

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!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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