Sam packed 320 marbles into four boxes, labelled A, B, C and D. Box A had the most
number of marbles and Box D had the least. The difference in the number of marbles
between Box A and the number of marbles in the other three boes were 8, 13 and 19.
How many marbles were there in Box D?
A + (A-8) + (A-13)+ (A-19) = 320
4 A - 40 = 320
4 A = 360
A = 90
90 - 19 = 71
Let's solve this step-by-step:
1. We are given that Sam packed 320 marbles into four boxes: A, B, C, and D.
2. The difference in the number of marbles between Box A and the other three boxes are 8, 13, and 19.
3. Let's assume the number of marbles in Box A is "x".
4. According to the information given, the number of marbles in Box B would be (x - 8), in Box C would be (x - 13), and in Box D would be (x - 19).
5. Now, we can set up an equation to solve for x. The sum of the marbles in the four boxes must be equal to 320: x + (x - 8) + (x - 13) + (x - 19) = 320.
6. Simplifying the equation: 4x - 40 = 320.
7. Adding 40 to both sides: 4x = 360.
8. Dividing both sides by 4: x = 90.
9. So Box A has 90 marbles, Box B has (90 - 8) = 82 marbles, Box C has (90 - 13) = 77 marbles, and Box D has (90 - 19) = 71 marbles.
Therefore, there were 71 marbles in Box D.
To find the number of marbles in Box D, we need to compare the difference between the number of marbles in Box A and the number of marbles in each of the other three boxes. Let's break it down step by step:
1. Let's assume the number of marbles in Box A is x.
2. The difference between the number of marbles in Box A and Box B is 8. So, the number of marbles in Box B is x - 8.
3. The difference between the number of marbles in Box A and Box C is 13. So, the number of marbles in Box C is x - 13.
4. The difference between the number of marbles in Box A and Box D is 19. So, the number of marbles in Box D is x - 19.
Now, we know that Sam packed a total of 320 marbles into the four boxes. Therefore, we can create an equation:
x + (x - 8) + (x - 13) + (x - 19) = 320
Simplifying the equation:
4x - 40 = 320
Adding 40 to both sides:
4x = 360
Dividing both sides by 4:
x = 90
Now that we know the number of marbles in Box A is 90, we can find the number of marbles in Box D:
x - 19 = 90 - 19 = 71
Therefore, there are 71 marbles in Box D.