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more pupils in school A than School B

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There are more pupils in schl A than Schl B. 30% of the pupils in schl A is 45 more than 40% ofthe pupils in schl B. If 10% of the pupils in school A leaves to join schl B,there will be 200 more pupils in schl A than schl B.
How many pupils are there in schl B.
How many percent less pupils are there in schl B than in schl A. Leave your answer as fraction in the simplest form.

Julian had 300 more cards than faizal. Julian gave 3/5 of his cards to faizal. Faizal then gave 1/4 of the total number of what he had then to Julian. In the end Faizal had 300 more cards than julian. How many cards did Julian have at first?

A basketball is thrown from a height of 20 metres. after each bounce, it only reaches half the height of the previous bounce. when the ball touches the gound for the third time, how much vertical distance has it moved.

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Jan 06, 2011
Math - Word Problem 1
by: Staff

The question:
by Judy

Problem 1: There are more pupils in schl A than Schl B. 30% of the pupils in schl A is 45 more than 40% ofthe pupils in schl B. If 10% of the pupils in school A leaves to join schl B,there will be 200 more pupils in schl A than schl B.
How many pupils are there in schl B.
How many percent less pupils are there in schl B than in schl A. Leave your answer as fraction in the simplest form.

The answer:

(Since I only have a maximum of 3000 characters I can use, I must eliminate about half of the detailed steps.The most important part of this problem is setting up the two equations, so I have tried to keep the most detail there.)

This problem can be solved by writing two equations. Each equation will have two unknowns.

Defining the unknowns:

X = number of students in school A
Y = number of students in school B

Write the two equations. Write down each sentence from the statement of the problem . . . one at a time. Convert each sentence to a mathematical statement (in this case, an equation):

The first equation:

30% of the pupils in schl A is 45 more than 40% of the pupils in schl B.
(30% times the number of students in school A = 40% of the number of students in school B + another 45% of the 40%)

30% * X = 40% * Y + 45

Convert the percents to their decimal equivalents (divide the % by 100):

.3 * X = .4 * Y + 45

The second equation:

If 10% of the pupils in school A leaves to join schl B (which will add 10% * X pupils to school B), there will be 200 more pupils in schl A than schl B.

X - 10% * X = Y + 10% * X + 200

Convert the percents to their decimal equivalents (divide the % by 100):

X - .1 * X = Y + .1 * X + 200

We now have two equations with two unknowns. This is just what we need to solve the problem.

.3 * X = .4 * Y + 45

X - .1 * X = Y + .1 * X + 200

Now it’s just a matter of solving the two equations for X & Y

1st equation – no further simplification is necessary

.3 * X = .4 * Y + 45

2nd equation – simplify

.8 * X = Y + 200

The final (simplified) versions of equations 1 & 2 are:

.3 * X = .4 * Y + 45

.8 * X = Y + 200


I am going to solve for X using the addition/subtraction method.

To begin, multiply equation two by .4 (each side of the equation). This will transform the Y on the right hand side of the equation to .4 * Y (which is what I need when I subtract the two equations). Next, multiply the second equation by -1.

Solving for X by subtracting the two equations:

X = 1750, school A has 1750 pupils


Now, solve for the number of students in school B. Substitute the 1750 for X in either of the two original equations, then solve for Y.

Y = 1200, school B has 1200 pupils


Calculate how many % less pupils school B has when compared to school A

% = [(1750 – 1200)/1750] * 100

% = 31.43

The final answer, part 1:

School A has 1750 pupils.
School B has 1200 pupils.

School B has 31.43% fewer students than School A.

Thanks for writing.

Staff
www.solving-math-problems.com


Jan 06, 2011
math - 2nd question
by: Staff

The question:
by Judy


Problem 2: Julian had 300 more cards than faizal. Julian gave 3/5 of his cards to faizal. Faizal then gave 1/4 of the total number of what he had then to Julian. In the end Faizal had 300 more cards than julian. How many cards did Julian have at first?



The answer:


Problem 2:

J = number of cards Julian had at first

F = number of cards Faizal had at first


Beginning - Julian had 300 more cards than Faizal.

J = F + 300


Julian gave 3/5 of his cards to Faizal.


Faizal then gave 1/4 of the total number of what he had then to Julian.


In the end Faizal had 300 more cards than Julian.

How many cards did Julian have at first?
J = number of cards initially held by Julian
F= number of cards initially held by Faizal

J = F + 300
Julian gives 3/5 of his cards to Faizal

Julian now has only 2/5 of his original cards
= (2/5)*(F+300)
= .4*(F+300)
= .4*F+120

Faizal has received 3/5 of Julian’s cards
=F+.6(F+300)
=F+.6F+180
=1.6F+180

Faizal now gives Julian ¼ of his cards, leaving Faizal with on ¾ of those cards
=1.6F+180
=-.25*(1.6F+180)
=.75*(1.6F+180)
= 1.2F+135
Faizal’s final number of cards = 1.2F+135

Julian has received 1/4 of Faizal’s cards
=.4*F+120+.25*(1.6F+180)
=.4*F+120+.4F+45
=.8*F+165
Julian’s final number of cards = .8*F+165


Final equation: Faizal has 300 more cards than Julian

Final number of cards held by Faizal - Final number of cards held by Julian = 300
(1.2F+135) – (.8*F+165) = 300
1.2F+135 –.8*F-165 = 300
.4F-30 = 300
.4F = 330
F = 825, Faisal had 825 cards at the beginning.
Julian had 1125 cards at the beginning (300 more than Faisal).





At first, Julian had 1125 cards and Faizal had 825 cards.

In the end, Julian had 825 cards and Faizal had 1125 cards.





Thanks for writing.


Staff
www.solving-math-problems.com


Jan 07, 2011
Math - 3rd question
by: Staff

The question:
by Judy


Problem 3: A basketball is thrown from a height of 20 metres. after each bounce, it only reaches half the height of the previous bounce. when the ball touches the gound for the third time, how much vertical distance has it moved.

The answer:

1st bounce: 20 metres down
2nd bounce: 10 metres up + 10 metres down
3rd bounce: 5 metres up + 5 metres down

Total vertical distance traveled (up and down) = 50 metres


Thanks for writing.


Staff
www.solving-math-problems.com


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