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[eric2010]

thx, i need the steps .

[CoffeeCat]

I will solve using algebra. Let the amt of water in tank X & Y be x and y respectively.

Volume of tank Y = x+y -26
volume of tank X = x+ y -8
From here i use v to represent (x+y), because what x and y is wouldn’t matter,.
using the ratio, v-26= (3/5) * (v-8)
5v - 130 = 3v -24
2v= 106
v=53
Total volume of Tank X + Y = 2v - (26+8) = 2v -34 = 72
Water needed = 72 - 53 = 19.

[mathsguru]

eric2010:

Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X unitl the water in Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If water from Tank X is poured into Tank Y until the water in Tank Y reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim ?

Hi Eric2010,

Here's my solution. Hope you can understand the diagrams...

Cheers,
MathsGuru

http://www.postimage.org/image.php?v=TsIeCbA

[persistent]

Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X until the water in Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If water from Tank X is poured into Tank Y until the water in Tank Y reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim?



Scenario 1

…Tank X…Tank Y
Before…5 u - A…8 l + A\t\t\t\t
\t\t
…+ A…- A
\t\t
…

After…5 units…8 l
…



Scenario 2

…Tank X…Tank Y
Before…\t26 l + B…\t3 u - B
\t\t
…- B…+ B
\t\t
…

After…26 l…3 units
…


5 u – A = 26 l + B
5 u – 26 l = A + B


8 l + A = 3 u – B
A + B = 3 u – 8 l

5 u – 26 l = 3 u – 8 l
5 u – 3 u = 26 l – 8 l
2 u = 18 l
1 u = 9 l


Ans. A + B = 3 x 9 l – 8 l = 19 l

[persistent]

Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X until the water in Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If water from Tank X is poured into Tank Y until the water in Tank Y reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim?



Scenario 1

…Tank X…Tank Y
Before…5 u - A…8 l + A\t\t\t\t
\t\t
…+ A…- A
\t\t
…

After…5 units…8 l
…



Scenario 2

…Tank X…Tank Y
Before…\t26 l + B…\t3 u - B
\t\t
…- B…+ B
\t\t
…

After…26 l…3 units
…


5 u – A = 26 l + B
5 u – 26 l = A + B


8 l + A = 3 u – B
A + B = 3 u – 8 l

5 u – 26 l = 3 u – 8 l
5 u – 3 u = 26 l – 8 l
2 u = 18 l
1 u = 9 l


Ans. A + B = 3 x 9 l – 8 l = 19 l

[P5G]

eric2010:

Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X unitl the water in Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If water from Tank X is poured into Tank Y until the water in Tank Y reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim ?

[ ][ ][ ][ ][ ] ..................Tank X
[ ][ ][ ] ........................... Tank Y


[ ........ ][ ] ..................Water in Tank X
[8][ ] ................................ Water in Tank Y

[ 26 ][ ]\t....................... Water in Tank X\t\t\t\t
[ ][ ] .............................Water in Tank Y


[ 26 ][ ][ ]\t\t
[8][ ][ ]

2u -- 26 - 8 = 18
1u -- 18/2 = 9
3u -- 9 x 3 = 27
27 - 8 = 19 litres

19 more litres to fill both tanks to their brim.

[P5G]

P5G:

eric2010:

Tanks X and Y are each filled with some water. If water from Tank Y is poured into Tank X unitl the water in Tank X reaches the brim, there will be 8 litres of water left in Tank Y. If water from Tank X is poured into Tank Y until the water in Tank Y reaches the brim, there will be 26 litres of water left in Tank X. The ratio of the volume of Tank X to the volume of Tank Y is 5:3. How many more litres of water are needed to fill both tanks to their brim ?

[ ][ ][ ][ ][ ] ..................Tank X
[ ][ ][ ] ........................... Tank Y


[ ........ ][ ] ..................Water in Tank X
[8][ ] ................................ Water in Tank Y

[ 26 ][ ]\t....................... Water in Tank X\t\t\t\t
[ ][ ] .............................Water in Tank Y


[ 26 ][ ][ ]\t...... 5u\t
[8][ ][ ] ............. 3u

2u -- 26 - 8 = 18
1u -- 18/2 = 9
3u -- 9 x 3 = 27
27 - 8 = 19 litres

19 more litres to fill both tanks to their brim.

[pineapple tarts]

Dear Mathsguru,


Aiyoh, I thot I am very clever with such questions already. Sikali I got stuck with this one. Pls help me.

There are 50 and pen and pencil. Each pen cost $6 and each pencil cost $5. The total cost is $47 MORE THAN the total cost of the pencil. How many pen and how many pencil are there?

[pineapple tarts]

Dear Mathsguru,


Another one. I am seeing stars…

There are 100 fruit tarts for 100 people. Each adult had 3 fruit tarts and every 3 children share one fruit tart. How many children are there?

[CoffeeCat]

pineapple tarts:

Dear Mathsguru,


Aiyoh, I thot I am very clever with such questions already. Sikali I got stuck with this one. Pls help me.

There are 50 and pen and pencil. Each pen cost $6 and each pencil cost $5. The total cost is $47 MORE THAN the total cost of the pencil. How many pen and how many pencil are there?

This is a typical chicken-ducks head&leg question.
The best way to go about solving without using algebra or guess and check is to make a supposition, that you have 50 pens (pen because it is more expensive).
In this case the total cost of the pens are $300. and it is $300 more than the total cost of pencils (there are no pencils).
So what happens when we interchange 1 pen for 1 pencil.
The total cost of pens will decrease by $6 . The total cost of pens will be $300-$6-$5 = 300-11.
therefore to find the number of pencils interchanged, (300-47)/11 = 253/11= 23.