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 there in the library?
X Fiction Books.
(x-240) Non-fiction Books
(x-240)-190 Picture Books.
x + (x-240) + (x-240)-190 = 2630 Books.
x + x-240 + x-240-190 = 2630
3x -480 - 190 = 2630
3x = 2630+670 = 3300
X = 1100
(X-240) = 860
(X-240)-190 = 670
670
To solve this problem, we'll create a system of equations based on the information given.
Let's say we have:
F = the number of fiction books
NF = the number of non-fiction books
P = the number of picture books
From the given information, we know the following relationships:
1) The number of non-fiction books is 240 fewer than the number of fiction books, so NF = F - 240.
2) The number of non-fiction books is 190 more than the number of picture books, so NF = P + 190.
3) The total number of books is 2630, so F + NF + P = 2630.
Now we can substitute the values from equation 1 and equation 2 into equation 3 to solve for the unknowns:
F + (F - 240) + (P + 190) = 2630
Simplifying the equation:
2F + P + 190 - 240 = 2630
2F + P - 50 = 2630
2F + P = 2630 + 50
2F + P = 2680
Now we have two equations:
1) F + NF + P = 2630
2) 2F + P = 2680
We can solve these equations using substitution or elimination.
Let's use elimination. Multiply equation 1 by 2 to make the coefficients of P the same:
2F + 2NF + 2P = 5260
Now subtract equation 2 from this new equation:
(2F + P) - (2F + P) = 5260 - 2680
2NF = 2580
NF = 2580/2
NF = 1290
Now substitute the value of NF into equation 1 to solve for F:
F + 1290 + P = 2630
F + P = 2630 - 1290
F + P = 1340
From equation 2, we also have:
2F + P = 2680
Now we have two equations:
1) F + P = 1340
2) 2F + P = 2680
Let's subtract equation 1 from equation 2:
(2F + P) - (F + P) = 2680 - 1340
F = 1340
Now we know the number of fiction books is 1340. We can substitute this value into equation 1 to solve for P:
1340 + P = 1340
P = 0
Therefore, there are 1340 fiction books, 0 picture books, and 1290 non-fiction books in the library.