If a blue box has 5 times as many marbles as a red box and the blue box has 24 more marbles than the red box how many marbles are in each box?

If the number of marbles in the red box are x, then those in the blue box would be 5x.

5x - x = 24

Solve for x, then 5 x.

To solve this problem, let's assign variables to represent the number of marbles in each box. Let's say "R" represents the number of marbles in the red box, and "B" represents the number of marbles in the blue box.

We are given two pieces of information:
1. The blue box has 5 times as many marbles as the red box: B = 5R
2. The blue box has 24 more marbles than the red box: B = R + 24

Now we can set up a system of equations using these two pieces of information:

B = 5R
B = R + 24

Since we have two equations and two variables, we can solve this system of equations to find the values of R and B.

Substitute the value of B from the first equation into the second equation:

5R = R + 24

Next, we'll solve for R:

5R - R = 24
4R = 24
R = 24/4
R = 6

Now that we have the value of R, we can substitute it back into either of the original equations to find the value of B:

B = 5R
B = 5(6)
B = 30

Therefore, there are 6 marbles in the red box and 30 marbles in the blue box.