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Word Problems/to solve word problems using simultaneous linear equations

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Question
HEY I'M ASTINA. AND I WOULD LIKE TO ASK SOME QUESTIONS.IT WILL BE A GREAT FAVOUR TO ME !

1.ONE - THIRD THE SUM OF 2 NOS. IS 6 WHILE HALF THEIR DIFF.IS ALSO 6 FIND THE NOS.

2.6 PENCILS & 4 ERASERS COST Rs42 WHILE 2 PENCILS AND 6 ERASERS COST Rs21. FIND THE PRICE OF A PENCIL AND AN ERASER.

3.THE PRICE OF BRUSHES IS Rs27 MORE THAN THE PRICE OF 3 PENCILS WHILE THE PRICE OF 3 BRUSHES AND 5 PENCILS IS Rs40. FIND THE PRICES OF ONE BRUSH AND ONE PENCIL.

4.A BOAT FIRST TRAVELS 48 KM DOWNSTREAM AND 24 KM UPSTREAM IN 7 HRS. THEN IT TRAVELS FOR 9 HRS , GOING 48 KM UPSTREAM AND 36 KM DOWNSTREAM. FIND THE SPEED OF THE BOAT IN STILL WATER AND THE SPEED OF THE WATER CURRENT.

Answer
Hello Astina,

1. Let x=the larger of the two numbers, and y=the smaller number.
...Thus, (x+y)/3=6 AND (x-y)/2=6...now solve these for x & y
==> multiplying the 1st equation by 3 gives: x+y=18
==> multiplying the 2nd equation by 2 gives: x-y=12
Now add the two equations so the y's drop out: 2x=30 ==> x=15 ==> y=3

2. Let p=the cost of a pencil, and e=the cost of an eraser
...Thus, 6p+4e=42 AND 2p+6e=21
==> multiplying the 2nd equation by -3 gives -6p-18e=-63,
so when we add the two the p's drop out ==> -14e=-21 ==> e=3/2=1.5 ==> p=6

3. Let b=the price of a brush, p=the price of a pencil
...Thus, b=3p+27 AND 3b+5p=40...now substitute b=3p+27 into the 2nd equation
and solve for p...3(3p+27)+5p=40 ==> 9p+81+5p=40 ==> 14p=-41 NEGATIVE???!!!
Hmm, looks like something is wrong here!  Are you sure you typed the problem
without error?

4. Let x=the speed of the boat in still water, y=the speed of the current.
...Thus, the speed of the boat downstream is x+y and upstream is x-y.
Now use distance = rate X time or time = distance/rate
The time required for the boat to go downstream 48 km is 48/(x+y).
The time required to go upstream 24 km is 24/(x-y).
But the total time is 7 hrs, so we get the equation: 48/(x+y) + 24/(x-y) = 7
Similarly, using the other information, we get: 48/(x-y) + 36/(x+y) = 9
Solving these two for x & y gives x=10 km/hr and y=2 km/hr.

Let me know if you need help getting those two answers.

I hope this helps!

TTYL, 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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