The library has a total collection of 2630 books. The number of non-fiction books is 240 fewer than the number of fiction books but 190 more than the number of picture books. How many books of each type are in the library?
Answers
Let x be the number of fiction books.
Let y be the number of non-fiction books.
Let z be the number of picture books.
From the first given, the total number of books is 2630. Therefore, x + y + z = 2630 (1)
From the second given, the number of non-fiction books is 240 fewer than the number of fiction books. Therefore, y = x-240 (2)
From the third given, the number of non-fiction books is 190 more than the number of picture books. Therefore, y = z + 190 (3)
Substitute equation (3) in equation (2):
z + 190 = x-240
z = x-430 (4)
Substitute equations (2) and (4) in equation (1):
x + (x-240) + (x-430)=2630
3x-670 = 2630
3x = 3300
x = 1100
Substitute by x in equation (2): y = 1100-240 = 860.
Therefore, z = 2630-x-y = 2630-1100-860 = 670.
Therefore, the number of fiction books is 1100, the number of non-fiction books is 860 and the number of picture books is 670.