A big box can hold 12 marbles and a small box can hold 5 marbles. There area total of 99 marbles. How many big boxes are there?
There are two unknowns: big and small boxes. Need to guess one.
However, if there are 3 small boxes, there would be 7 large boxes.
(12*7) + (3*5) = 99
Well, let's do some mathematical clownery! If we call the number of big boxes B and the number of small boxes S, we can set up a couple of equations.
Equation 1: B + S = total number of boxes
Equation 2: 12B + 5S = 99 marbles
Now, let's solve these equations. If we multiply Equation 1 by 12, we get:
12B + 12S = 12 times the total number of boxes
Subtracting Equation 2 from this gives us:
7S = 12 times the total number of boxes - 99 marbles
Now, since we know that both B and S are whole numbers, we can substitute different values for the total number of boxes and see if it works. After some clownish attempts, we find that if there are 3 big boxes and 9 small boxes, we get 7 + 12(9) = 99.
So, the answer is 3 big boxes!
To solve this problem, we can use algebra.
Let's assume the number of big boxes is represented by "B," and the number of small boxes is represented by "S."
According to the given information, each big box can hold 12 marbles, so the total number of marbles in the big boxes is 12B.
Similarly, each small box can hold 5 marbles, so the total number of marbles in the small boxes is 5S.
And we know that the total number of marbles is 99. So we can set up the equation:
12B + 5S = 99
Now, we need to find the value of B.
To solve for B, we need to consider the constraints involved. The number of big and small boxes cannot be negative or fractional, so we are looking for a whole number solution.
We can use trial and error to find the solution that satisfies the given equation.
Let's start with assuming there are 5 big boxes (B = 5):
12 * 5 + 5S = 99
60 + 5S = 99
5S = 99 - 60
5S = 39
S = 39 / 5
S ≈ 7.8
From this trial, we can see that 5 big boxes and 7.8 small boxes do not satisfy the given equation. Since we are looking for whole number solutions, we can conclude that 5 big boxes are not the correct answer.
Let's try assuming there are 6 big boxes (B = 6):
12 * 6 + 5S = 99
72 + 5S = 99
5S = 99 - 72
5S = 27
S = 27 / 5
S = 5.4
Again, we see that 6 big boxes with 5.4 small boxes is not a valid solution.
Let's try assuming there are 7 big boxes (B = 7):
12 * 7 + 5S = 99
84 + 5S = 99
5S = 99 - 84
5S = 15
S = 15 / 5
S = 3
This time, when there are 7 big boxes and 3 small boxes, the equation is satisfied.
Therefore, the solution is B = 7. There are 7 big boxes.
To find the number of big boxes, we need to determine how many times the big box can be filled completely with marbles.
First, let's find the maximum number of marbles that can fit in the big boxes:
The big box can hold 12 marbles.
Now, let's divide the total number of marbles (99) by the maximum number of marbles that can fit in the big boxes (12):
99 ÷ 12 = 8 with a remainder of 3.
Since we can't have a fraction of a box, we take the whole number from the division, which is 8. Therefore, there are 8 big boxes.
So, the answer is 8 big boxes.