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Picture a vivid scene of a playroom. Divided into two sections are two large boxes, one labeled 'Box A' and the other, 'Box B'. Prior to any movement of marbles, 'Box A' is densely filled with marbles that there are seven times the number of marbles in 'Box B'. A young girl, let's imagine her to be Hispanic and wears a red dress with white polka dots, is in the act of shifting 294 bright, shiny marbles from Box A to Box B. After her action, the marbles are distributed equally between the two boxes.

There were 7 times as many marbles in Box A as in Box B. After Joyce transferred 294 marbles from Box A to Box B, both boxes had the same number of marbles. How man marbles were there in Box A at first.

a = 7b

a-294 = b+294

7b-294 = b+294
6b = 588
b = 98
so, a=7b=686

check: 686-294 = 98+294 = 392

To Steve;I don’t understand.how did you manage to get 588?

Steve got 588 by cancelling out 1 b

I'll break it down, try to follow.....
Example:
7b-294 = b+294
7b = b+294+294
7b = b+588
-------------------
6b = +588
588/6 = 98
1b = 98

Ah, the curious case of the sneaky marbles! Let me juggle the numbers for you:

Let's say the number of marbles in Box B was x. According to the riddle, there were 7 times as many marbles in Box A, so we can say there were 7x marbles in Box A.

But then the sneaky Joyce came along and transferred 294 marbles from Box A to Box B. Now, both boxes have the same number of marbles.

So, if we subtract 294 from the original count of marbles in Box A, we get 7x - 294, which should equal x. We can set up an equation:

7x - 294 = x

Now, let me summon my funny math skills to solve it:

6x = 294

x = 49

Voila! Box B started with 49 marbles. But, since there were 7 times as many marbles in Box A, that means Box A started with 7 times 49 marbles, which is... *drumroll*... 343!

So, there were 343 marbles in Box A at first. But did they behave themselves or did they try to roll away? That's a mystery only the marbles can answer!

To solve this problem, let's break it down step-by-step.

Let's assume that the initial number of marbles in Box B is x.

According to the problem, there were 7 times as many marbles in Box A as in Box B. Therefore, the initial number of marbles in Box A would be 7x.

After transferring 294 marbles from Box A to Box B, the number of marbles in both boxes became equal. This can be represented as:

7x - 294 = x + 294

Now, let's solve this equation to find the initial number of marbles in Box A.

Subtract x from both sides of the equation:

6x - 294 = 294

Add 294 to both sides of the equation:

6x = 588

Divide both sides of the equation by 6:

x = 98

So, the initial number of marbles in Box A was 7x, which is 7 * 98 = 686.

Therefore, there were 686 marbles in Box A at first.

It ether 47 50 48 45