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 many marbles were there in box a at first?

a=7b

a-294 = b+294
a = 686

135688

Well, let's start by solving this marble mystery! Since there were 7 times as many marbles in box A as in box B, let's say box B had "x" marbles. So, box A had 7 times "x," which means it had 7x marbles.

After Joyce transferred 294 marbles from box A to box B, we need to find the new number of marbles in each box. Let's say there are "y" marbles left in box A. That means box B now has "x + 294" marbles.

Since both boxes had the same number of marbles after the transfer, we can set up an equation: 7x - 294 = x + 294.

Now, let's solve this with a little laughter! A marble joke to keep us entertained while we do the math:

Why were the marbles so well-behaved?
Because they were always on their best marbleous behavior!

Okay, back to business. Let's solve the equation:

7x - 294 = x + 294

Subtracting "x" from both sides:
6x - 294 = 294

Adding 294 to both sides:
6x = 588

Dividing both sides by 6:
x = 98

So, at first, box B had 98 marbles. Since there were 7 times as many marbles in box A, that means box A had 7 * 98 = 686 marbles.

Voila! Box A started with 686 marbles. Keep the laughter rolling!

Let's assume that the initial number of marbles in box b is x.

Since there were 7 times as many marbles in box a as in box b, the initial number of marbles in box a is 7x.

After Joyce transferred 294 marbles from box a to box b, the number of marbles in box a is now 7x - 294, and the number of marbles in box b is now x + 294.

Since both boxes had the same number of marbles after the transfer, we can set up the equation:

7x - 294 = x + 294

To solve for x, we can simplify the equation by combining like terms:

6x = 588

Dividing both sides of the equation by 6, we find that x = 98.

Therefore, the initial number of marbles in box a was 7x = 7 * 98 = 686 marbles.

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

1. Let's assume the initial number of marbles in box b is "x".
So, the initial number of marbles in box a is 7 times x, which is 7x.
Therefore, at first, box a had 7x marbles and box b had x marbles.

2. According to the problem, Joyce transferred 294 marbles from box a to box b.
After the transfer, both boxes had the same number of marbles.
So, the number of marbles in box a is now 7x - 294, and the number of marbles in box b is now x + 294.

3. Since both boxes now have the same number of marbles, we can set up an equation:
7x - 294 = x + 294

4. Let's solve this equation to find the value of x:
7x - x = 294 + 294
6x = 588
x = 588 / 6
x = 98

5. Now that we know x is 98, we can find the initial number of marbles in box a:
Initial number of marbles in box a = 7x = 7 * 98 = 686

Therefore, there were 686 marbles in box a at first.