a local resturant sells muffins in boxes of 6, 9, and 20.
determine whether the following amounts of muffins can be purchased. number of drsired muffins 15,99, 19, 48,76
15 = 6+9
99 = 9*11
48 = 8*6
76 = 2*20 + 4*9
19 can't be made
To determine whether the listed amounts of muffins can be purchased in boxes of 6, 9, or 20, we can use a combination of division and remainder operation.
Let's go through each number:
1. 15 muffins: We can check if 15 can be divided evenly by any of the box sizes. If we divide 15 by 6, we get a remainder of 3. If we divide 15 by 9, we get a remainder of 6. If we divide 15 by 20, we get a remainder of 15. Thus, 15 muffins cannot be purchased using any combination of these boxes.
2. 99 muffins: Similar to the previous case, we can check if 99 can be divided evenly by any of the box sizes. Dividing 99 by 6 gives a remainder of 3. Dividing 99 by 9 gives a remainder of 0. Dividing 99 by 20 gives a remainder of 19. Thus, 99 muffins can be purchased using boxes of 9.
3. 19 muffins: By dividing 19 by 6, we get a remainder of 1. If we divide 19 by 9, we also get a remainder of 1. However, if we divide 19 by 20, we get a remainder of 19. Therefore, 19 muffins cannot be purchased using any combination of these boxes.
4. 48 muffins: Dividing 48 by 6 gives a remainder of 0. Dividing 48 by 9 also gives a remainder of 0. Dividing 48 by 20 gives a remainder of 8. Thus, 48 muffins can be purchased using boxes of either 6 or 9.
5. 76 muffins: If we divide 76 by 6, we get a remainder of 4. If we divide 76 by 9, we get a remainder of 4. Dividing 76 by 20 gives a remainder of 16. Thus, 76 muffins can be purchased using boxes of either 6 or 9.
To summarize:
- 15 muffins cannot be purchased using boxes of 6, 9, or 20.
- 99 muffins can be purchased using boxes of 9.
- 19 muffins cannot be purchased using boxes of 6, 9, or 20.
- 48 muffins can be purchased using boxes of 6 or 9.
- 76 muffins can be purchased using boxes of 6 or 9.