There are 30 books in a bookcase. The books in the case are either math, science ,or history books. Ten of the books are math books. There are 6 fewer science books than history books. How many science books are in the bookcase??????

m+s+h=30

10+s+h=30
10+(h-6)+h=30
solve for h
than, s=h+6

To determine the number of science books in the bookcase, let's break down the information provided step by step.

We are given:
- There are 30 books in total.
- There are 10 math books.
- The number of science books is 6 fewer than the number of history books.

Let's assign variables to the unknowns:
- Let's use "m" to represent the number of math books.
- Let's use "s" to represent the number of science books.
- Let's use "h" to represent the number of history books.

From the given information, we have:

1. The total number of books:
m + s + h = 30

2. The number of math books:
m = 10

3. The number of science books is 6 fewer than the number of history books:
s = h - 6

Now, let's substitute the known values into the equations:

m + s + h = 30 (Substitute m = 10 into this equation)
10 + s + h = 30 (Equation 1)

s = h - 6 (Equation 2)

Now we have a system of two equations with two unknowns. We can solve this system using substitution or elimination.

Let's use substitution method:

From Equation 2, we can express h in terms of s:
h = s + 6

Now substitute the value of h in Equation 1:

10 + s + (s + 6) = 30

Combine like terms:

2s + 16 = 30

Subtract 16 from both sides:

2s = 14

Divide both sides by 2:

s = 7

Therefore, there are 7 science books in the bookcase.