Tutor MathsGuru: Ask me for your burning Maths questions!

[Dharma]

firebird:

Dear mathsguru


Good morning.

Please help me on the following question:

1) There were 850 marbles in box A and 70 marbles in Box B. When an equal number of marbles were added into each box, the ratio of the number of marbles in A to that in B is 5:1.
How many marbles were added into both boxes?

I tried this quesion for an hour or so, I give up.

Many thanks
firebird

Box A : 850 + 1u =5p
Box B : 70 + 1u = 1p

5p - 850 = 1p - 70
4p = 850 - 70 = 780
1p = 195
No. of marbles added , 1u = 195 - 70 = 125

[starlight1968sg]

firebird:

1) There were 850 marbles in box A and 70 marbles in Box B. When an equal number of marbles were added into each box, the ratio of the number of marbles in A to that in B is 5:1.
How many marbles were added into both boxes?

I solved using the model pattern.

Since I don't know how to put my model diagram onto the web, I try to explain in details.

Draw the usual model for A (having 850 marbles) and B (having 70 marbles). Next draw a shaded area to represent the number of marbles added to each box.

We know after adding this number of marbles to each box, the ratio becomes 5:1.

This new model diagram for A becomes 5 parts and 1 part is for the new model diagram for B.

Now I part is actually 70 marbles plus the shaded area.

Can you see that for \"new\" A, it has 5 slots of each 70 marbles and 5 slots of shaded area? Now the tricky part is : 850 is equal to 5 slots of each 70 marbles AND 4 slots of shaded area.

850 - (5*70) = 850 - 350 = 500
500 / 4 = 125
This means the shaded area (= number of marbles added) = 125.

(a picture speaks thousand words!)

[firebird]

Dear Dharma and Starlight1968sg


Good morning.

Many thanks to both.

With best regards
firebird

[starlight1968sg]

help:

In a bag, there are red, yellow and blue marbles. There were twice as many red marbles as yellow marbles and twice as many yellow marbles as blue marbles at first. After removing 15 blue marbles and some yellow marbles from the bag, the number of red marbles became thrice that of the yellow marbles but the number of yellow marbles was still twice that of the blue marbles. What was the total number of marbles in the bag at first?[/size]

What is the answer?
Is it 315 marbles?
Am still struggling !

[Dharma]

starlight1968sg:

help:

In a bag, there are red, yellow and blue marbles. There were twice as many red marbles as yellow marbles and twice as many yellow marbles as blue marbles at first. After removing 15 blue marbles and some yellow marbles from the bag, the number of red marbles became thrice that of the yellow marbles but the number of yellow marbles was still twice that of the blue marbles. What was the total number of marbles in the bag at first?[/size]

What is the answer?
Is it 315 marbles?
Am still struggling !

315 is correct.

Red : 12u
Yellow : 6u – 1p = 4u
Blue : 3u – 15 = 2u

3u – 2u = 15
1u = 15
Total no. of marbles at first = 12u + 6u + 3u = 21u =21 x 15 = 315

[starlight1968sg]

Dharma:

315 is correct.

Red : 12u
Yellow : 6u – 1p = 4u
Blue : 3u – 15 = 2u

3u – 2u = 15
1u = 15
Total no. of marbles at first = 12u + 6u + 3u = 21u =21 x 15 = 315

Thanks.
I solved using the model diagram.

Is it convincing enough that the number of Yellow marbles taken is 15, so that the ratio for Yellow to Blue remains 2:1 ?

[Dharma]

starlight1968sg:

Dharma:

315 is correct.

Red : 12u
Yellow : 6u – 1p = 4u
Blue : 3u – 15 = 2u

3u – 2u = 15
1u = 15
Total no. of marbles at first = 12u + 6u + 3u = 21u =21 x 15 = 315

Thanks.
I solved using the model diagram.

Is it convincing enough that the number of Yellow marbles taken is 15, so that the ratio for Yellow to Blue remains 2:1 ?

To maintain the ratio of yellow to blue marbles of 2 : 1 but ratio of red to yellow marbles of 3 : 1, you need to remove 2 x 15 = 30 yellow marbles.

[starlight1968sg]

Dharma:

To maintain the ratio of yellow to blue marbles of 2 : 1 but ratio of red to yellow marbles of 3 : 1, you need to remove 2 x 15 = 30 yellow marbles.

YES!

I take each block (ie blue marbles) as \"remaining plus 15\". So for yellow block, it is \"remaing plus 15\" and \"remaing plus 15\" ie remove 15*2 = 30 yellow marbles.

Since the question says \"some yellow marbles\" are removed and to maintain the ratio of Yellow to Blue at 2:1, the number of yellow marbles removed has to be 15*2 = 30.

Though somehow am not very convinced about this part. Ok, maybe am just a bit slow to understand.

[Dharma]

starlight1968sg:

Dharma:

To maintain the ratio of yellow to blue marbles of 2 : 1 but ratio of red to yellow marbles of 3 : 1, you need to remove 2 x 15 = 30 yellow marbles.

YES!

I take each block (ie blue marbles) as \"remaining plus 15\". So for yellow block, it is \"remaing plus 15\" and \"remaing plus 15\" ie remove 15*2 = 30 yellow marbles.

Since the question says \"some yellow marbles\" are removed and to maintain the ratio of Yellow to Blue at 2:1, the number of yellow marbles removed has to be 15*2 = 30.

Though somehow am not very convinced about this part. Ok, maybe am just a bit slow to understand.

I’m no expert at models but I am able to explain to u what I have done.

Actually, the number of yellow marbles removed is irrelevant for answering this question, so don’t worry too much about it.

1.\tThe initial condition is ratio of red : yellow : blue = 4 : 2 : 1
2.\tFinal condition is ratio of red : yellow : blue = 6 : 2 : 1
3.\tNo red marbles are given out, so the no. of red marbles DO NOT change.
4.\tNow u have initial ratio of 12: 6 : 3 and final ratio of 12 : 4 : 2
5.\tFrom (4) u can see for every 1 unit reduction of blue marbles, there will be 2 units of reduction in yellow marbles, based on the ratios above.

[starlight1968sg]

Dharma:

I’m no expert at models but I am able to explain to u what I have done.


1.\tThe initial condition is ratio of red : yellow : blue = 4 : 2 : 1
2.\tFinal condition is ratio of red : yellow : blue = 6 : 2 : 1
3.\tNo red marbles are given out, so the no. of red marbles DO NOT change.
4.\tNow u have initial ratio of 12: 6 : 3 and final ratio of 12 : 4 : 2
5.\tFrom (4) u can see for every 1 unit reduction of blue marbles, there will be 2 units of reduction in yellow marbles, based on the ratios above.

Thanks.
Your solution is so short and clear. Earlier, I was struggling with the model diagram.
Myself is lousy in model & ratio. So I can't expect my dd to do well too. :stupid: