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.