Two bags contain the same number of marbles. In one bag, the ratio of black marbles to white marbles is 4:3. In the other bag, the ratio is 3:2. Which bag contains more black marbles?

Thanks!

Assume that there are 100 marbles in each bag.

Firstly divide 100 by 7 (ratio 4:3) 14.28.

Multiply 14.28 by 4 = 57.12 *57 marbles
Mulitply 14.28 by 3 = 42.84 *53 marbles

Secondly do the same for ratio 3:2

Divide 100 by 5 = 20

Multiply 20 by 3 = 60 marbles
Multiply 20 by 2 = 40 marbles.

Therefore the second bag contains more black marbles.

Hi Kelly,

For this one.

Multiply 14.28 by 3 = 42.84 *53 marbles

Do you mean to say *43 marbles? rounded up from 42.84?

Thanks for your help.

Change the ratio so that the second number is the same

4:3 = 8:6 , first # stands for black, 2nd # stands for white

3:2 = 9:6

clearly the 2nd has more black marbles

Hi Reiny,

Before posting this question, I thought the same way by putting the same amount of white marbles but if you add the total amount of marbles for both bags and that wouldn't be equal since the question mentioned "Two bags contain the same number of marbles".

4:3 = 8:6 (14 marbles)
3:2 = 9:6 (15 marbles)

Let me know if I'm wrong.

Thanks!

you say:

4:3 = 8:6 (14 marbles)
why not keep going...
14 marbles or 28 , or 42 , 56 , ....

3:2 = 9:6 (15 marbles)
why not keep going
15 marbles or 30, 45 , ...

when are they the same ?
What number divides by both 15 and 14 ?
210

So suppose each bag has 210 marbles
first bag: 4:3 ratio -- > 120 black to 90 white
2nd bag: 9:6 --> 126 black to 84 white

Thank you again.

Sorry Eric, yes I did mean 43 (typo sorry)

thanks!!!!!!!!!

To determine which bag contains more black marbles, we need to compare the two ratios and find the bag with the greater value for the black marbles.

Let's first calculate the ratio of black marbles to white marbles in each bag.

In the first bag, the ratio of black marbles to white marbles is 4:3. This means that for every 4 black marbles, there are 3 white marbles.

In the second bag, the ratio of black marbles to white marbles is 3:2. This implies that for every 3 black marbles, there are 2 white marbles.

Now, let's find the total number of marbles in each bag by considering the common denominator between the two ratios. We'll assume both bags have the same number of marbles.

The first bag has a ratio of 4:3. Since 4 + 3 = 7, the total number of parts in the ratio is 7. If we divide the total number of marbles in the bag equally into these 7 parts, each part would represent 1 marble. Therefore, the bag contains a total of 7 marbles (4 black marbles + 3 white marbles).

Similarly, the second bag has a ratio of 3:2, totaling 5 parts (3 black marbles + 2 white marbles). Therefore, the second bag contains a total of 5 marbles.

Finally, we compare the number of black marbles in each bag. In the first bag, we have 4 black marbles out of a total of 7 marbles. In the second bag, we have 3 black marbles out of a total of 5 marbles.

Thus, comparing the ratios, we see that the first bag contains more black marbles because it has 4 black marbles, whereas the second bag has only 3 black marbles.

Therefore, the first bag contains more black marbles than the second bag.