Mr. Smith has 17 18-cent notebooks and 7-cent pencils. The notebooks and pencils are worth $1.85. How many notebooks and how many pencils does Mr. Smith have?
number of notebooks : n
number of pencils : 17-n
18n + 7(17-n) = 185
solve ...
I still can't solve it. I am getting stuck.
What grade level is this ???
18n + 7(17-n) = 185
18n + 119 - 7n = 185
11n = 66
n = 6
so 6 notebooks and 11 pencils
check: 6x18 + 11x7 = 185
To solve this problem, we need to set up a system of equations representing the given information.
Let's assume that Mr. Smith has 'x' notebooks and 'y' pencils.
According to the given information:
1. Mr. Smith has 17 18-cent notebooks, so the value of the notebooks can be expressed as 17 * 18 = 306 cents.
2. Mr. Smith has 7-cent pencils, so the value of the pencils can be expressed as 7y cents.
3. The total value of the notebooks and pencils is $1.85, which is equal to 185 cents.
So, we can write the first equation as: 306 + 7y = 185 (equation 1)
And the second equation is: x + y = 17 (equation 2)
To solve this system of equations, we can use the substitution method.
Let's solve equation 2 for x:
x = 17 - y
Now we substitute this value of x in equation 1:
306 + 7y = 185
Subtract 306 from both sides:
7y = 185 - 306
7y = -121
Divide by 7:
y = -121 / 7
y = -17
Since Mr. Smith cannot have a negative number of pencils, we discard this solution. It means there is no solution in which he has exactly 17 notebooks and 7 pencils.
Therefore, we can conclude that there is no possible combination of notebooks and pencils that satisfies the given information.