Question

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Jason put 27 pictures on six pages of his album. Each page holds 3 large, 4 medium or 6 small pictures. He had some pictures of each size. How many pictures of each size did he have?

Answer 1

Let's assume that Jason had x large pictures, y medium pictures, and z small pictures.

According to the given information, each page can hold a total of 3 large, 4 medium, or 6 small pictures. Since there are 6 pages in total, the total number of large pictures can be calculated by multiplying 3 by 6:

Total large pictures = 3 * 6 = 18

Similarly, the total number of medium pictures can be calculated by multiplying 4 by 6:

Total medium pictures = 4 * 6 = 24

And the total number of small pictures can be calculated by multiplying 6 by 6:

Total small pictures = 6 * 6 = 36

Now, we can set up three equations based on the given information:

x + y + z = 27 (equation 1: total number of pictures)

x = 18 (equation 2: total number of large pictures)

y = 24 (equation 3: total number of medium pictures)

By substituting equations 2 and 3 into equation 1, we have:

18 + 24 + z = 27

Simplifying the equation:

42 + z = 27

Subtracting 42 from both sides:

z = 27 - 42

z = -15

From the third equation, we can conclude that z, the number of small pictures, is -15. However, this does not make sense since we cannot have a negative number of pictures. Therefore, we need to revise our solution.

Since we cannot have a negative number of pictures, it means that Jason must have had fewer small pictures than his album could hold.

Let's try a smaller number of small pictures and see if it makes sense. Let's assume Jason had 3 small pictures.

By substituting x = 18 and y = 24 into equation 1:

18 + 24 + 3 = 27

42 + 3 = 27

45 = 27

This equation is not true, which means our assumption that Jason had 3 small pictures is incorrect.

Let's try a larger number of small pictures and see if it makes sense. Let's assume Jason had 5 small pictures.

By substituting x = 18 and y = 24 into equation 1:

18 + 24 + 5 = 27

42 + 5 = 27

47 = 27

Again, this equation is not true, which means our assumption that Jason had 5 small pictures is incorrect as well.

By analyzing the situation, we can conclude that there is no whole number solution that satisfies the given conditions. It seems that there might be an error in the problem or the numbers provided.