A store sells small notebooks for $7 and large notebooks for $10. If a student buys 6 notebooks and spends $54, how many of each size did he buy?
small books --- x
large books = 6-x
7x + 10(6-x) = 54
solve for x, and state your conclusion
Let's assume the number of small notebooks the student bought is represented by "x".
Let's further assume the number of large notebooks the student bought is represented by "y".
According to the given information:
The cost of each small notebook is $7, so the total cost of small notebooks would be 7x.
The cost of each large notebook is $10, so the total cost of large notebooks would be 10y.
The total number of notebooks the student bought is 6, so we can write the equation:
x + y = 6 ---(1) (equation representing the total number of notebooks)
The total cost spent by the student is $54, so we can write the equation:
7x + 10y = 54 ---(2) (equation representing the total cost spent)
Now, we can solve this system of equations to find the values of x and y.
To solve equation (1) for x, we can rewrite it as:
x = 6 - y ---(3)
Substituting equation (3) into equation (2), we get:
7(6 - y) + 10y = 54
42 - 7y + 10y = 54
42 + 3y = 54
3y = 12
y = 4
Now, substituting the value of y into equation (3), we get:
x = 6 - 4
x = 2
Therefore, the student bought 2 small notebooks and 4 large notebooks.
To solve this problem, let's assign variables to represent the number of small notebooks and large notebooks the student bought.
Let's say:
- Let 's' be the number of small notebooks.
- Let 'l' be the number of large notebooks.
We can now formulate two equations based on the given information:
1. The total number of notebooks bought: s + l = 6
2. The total amount spent: 7s + 10l = 54
Now, we can solve these equations simultaneously to find the values of 's' and 'l'.
To start, let's solve equation (1) for 's':
s = 6 - l
Substitute this value of 's' into equation (2):
7(6 - l) + 10l = 54
Now simplify the equation:
42 - 7l + 10l = 54
-7l + 10l = 54 - 42
3l = 12
l = 12 / 3
l = 4
Now that we know l = 4, we can substitute this value into equation (1):
s + 4 = 6
s = 6 - 4
s = 2
Therefore, the student bought 2 small notebooks and 4 large notebooks.