# Thread: Maths method 11 Linear equation problem solving

1. ## Maths method 11 Linear equation problem solving

Hello I've received holiday homework from my text book and i cant seem to work ou these questions. anyone know the working outs?i saw the answer from the back of the book but i don't just want to copy it i want to understand it

thanks.:]

1)Two tanks contain equal amounts of water. They are connected by a pipe and 3000 litres of water is pumped from one tank to the other. One tank then contains 6 times as much water as the toher. How many litres of water did each tank contain originally.

2)a boy is 24 years younger than his father. In 2 years time the sum of thier ages will be 40. find the present ages of father and son.

3)A man travels from A to B at 4km/h and from B to A at 6km/h. the total journey takes 45 minutes. find the distance traveled

4) jess walked for 45 minutes at 3km/h and then ran for half an hour at xkm/h. At the end of that time she was 6km from the starting point. find the value of x.

2. Originally Posted by fresh_
2)a boy is 24 years younger than his father. In 2 years time the sum of thier ages will be 40. find the present ages of father and son.

Let the son's age be x. Then we know that the father's age is x + 24 years old.

In two years the boy will be x + 2 years old and the father x + 24 + 2 = x + 26 years old. Then we know that
$(x + 2) + (x + 26) = 40$

$2x + 28 = 40$

$2x = 12$

$x = 6$

-Dan

3. Originally Posted by fresh_
3)A man travels from A to B at 4km/h and from B to A at 6km/h. the total journey takes 45 minutes. find the distance traveled

The relevant equation here is
$d = vt$

Let the distance from A to B (or B to A) be d.

From A to B we have
$d = 4t$
where t is the take it takes for the trip.

From B to A we have
$d = 6T$
where T is the time it takes for the trip.

And we also know that
$t + T = 45~min = \frac{3}{4}~h$

(Use the unit hours for the time since the speed is given in km/h.)

This gives you the three equations
$d = 4t$
$d = 6T$
$t + T = \frac{3}{4}$

-Dan

4. [QUOTE=fresh_;162147]Hello I've received holiday homework from my text book and i cant seem to work ou these questions. anyone know the working outs?i saw the answer from the back of the book but i don't just want to copy it i want to understand it

thanks.:]

1)Two tanks contain equal amounts of water. They are connected by a pipe and 3000 litres of water is pumped from one tank to the other. One tank then contains 6 times as much water as the toher. How many litres of water did each tank contain originally.

Let us say each tank has x liters of water initially.
So after 3000L is transfered from one tank to the other,
one tank has now (x -3000) liters, and the other has (x +3000) liters.

Then the problem says the tank with more water has now 6 times as much water than the tank with less water, meaning,
(x +3000) = 6*(x -3000)

So, simplifying that,
x +3000 = 6x -18,000
x -6x = -18,000 -3000
-5x = -21,000
x = -21,000 /(-5)
x = 4200L -------same as the book answer.

- - - - - - - -

4) jess walked for 45 minutes at 3km/h and then ran for half an hour at xkm/h. At the end of that time she was 6km from the starting point. find the value of x.

distance = rate * time
d = rt

The units must be consistent. If x is in km/hr, then time must be in hours.
45minutes = 45/60 = 3/4 hr.

(3/4)(3) +(1/2)(x) = 6 ------this is what the problem says.

So,
9/4 +x/2 = 6
Clear the fractions, multiply both sides by 4,
9 +2x = 24
2x = 24 -9
x = 15/2 = 7.5 ----------answer.

5. THANKS GUYS FOR THE HELP!!, I REALLY NEEDED IT

theirs one more i got stuck on for this exercise

a shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at$2.00 per dozen. He sells them all for $2.50 a dozen and makes$15 profit. how many dozens were there in each of the crates.

THANKS AGAIN

6. ## Here it is

Originally Posted by fresh_
a shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at$2.00 per dozen. He sells them all for $2.50 a dozen and makes$15 profit. how many dozens were there in each of the crates.
let there be x dozen eggs that he bought for 1.5$therfor his expenditure will be=1.5x$
now he bought 3 dozen more eggs than before i.e x+3 for 2$per dozen, therfor his expenditure will be=2(x+3)$
so his total expenditure is
[1.5x +2(x+3)]$now total dozen of eggs =x+x+3=2x+3 these were sold for 2.5$ per dozen therfor total selling price=2.5(2x+3) $(profit=total selling price-expenditure) profit is given to be=15$ therefor
2.5(2x+3)-[1.5x +2(x+3)]=15
5x+7.5-1.5x-2x-6=15
1.5x=13.5
x=9
so intially there were 9 dozen eggs. Since second time shopkeeper took 3 dozen more eggs than previous time so second time there were 9+3=12 dozen eggs

7. Originally Posted by nikhil
let there be x dozen eggs that he bought for 1.5$therfor his expenditure will be=1.5x$
now he bought 3 dozen more eggs than before i.e x+3 for 2$per dozen, therfor his expenditure will be=2(x+3)$
so his total expenditure is
[1.5x +2(x+3)]$now total dozen of eggs =x+x+3=2x+3 these were sold for 2.5$ per dozen therfor total selling price=2.5(2x+3) $(profit=total selling price-expenditure) profit is given to be=15$ therefor
2.5(2x+3)-[1.5x +2(x+3)]=15
5x+7.5-1.5x-2x-6=15
1.5x=13.5
x=9
so intially there were 9 dozen eggs. Since second time shopkeeper took 3 dozen more eggs than previous time so second time there were 9+3=12 dozen eggs
thanks but this bit
now total dozen of eggs =x+x+3=2x+3 how did you get the 3 ?