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?
I would like to see how this is solved, not just the answer, that way I can learn how to do it.
17=N+P
.18N+.07P=1.85
in the first equation solve for N
N=17-P
Put that into the second equation.
.18(17-P)+.07P=1.85
then solve for P. Once you have that,
N=17-P
Thank you so much for explaining.
To solve this problem, we can use a system of equations. Let's define the following variables:
Let N represent the number of notebooks Mr. Smith has.
Let P represent the number of pencils Mr. Smith has.
From the given information, we can set up two equations:
Equation 1: "Mr. Smith has 17 18-cent notebooks and 7-cent pencils."
N = 17
P = 7
Equation 2: "The notebooks and pencils are worth $1.85."
0.18N + 0.07P = 1.85
Now, let's solve the system of equations. We can start by substituting the values from Equation 1 into Equation 2:
0.18(17) + 0.07(7) = 1.85
3.06 + 0.49 = 1.85
3.55 = 1.85
This equation is not true, so there seems to be an error. Let's check our initial setup.
We realized that there was a mistake in the original problem statement. The given value of $1.85 cannot be achieved with the given prices of notebooks and pencils. Hence, there seems to be no solution to this problem.
Apologies for the confusion caused. If you have any other questions, feel free to ask.
To solve this problem, we can use a system of equations. Let's define the variables before proceeding with the steps:
Let n be the number of notebooks.
Let p be the number of pencils.
According to the information given:
1. Each notebook costs 18 cents.
2. Each pencil costs 7 cents.
3. Mr. Smith has a total of 17 notebooks and 7 pencils.
4. The total cost of all the notebooks and pencils is $1.85.
Now, let's translate this information into equations:
1. The cost of n notebooks can be calculated as 18n cents.
2. The cost of p pencils can be calculated as 7p cents.
3. The total cost of all notebooks and pencils is given as $1.85, which is equivalent to 185 cents.
Based on the above equations, we can write:
Equation 1: 18n + 7p = 185 (since the total cost is $1.85 or 185 cents)
Equation 2: n + p = 17 (since Mr. Smith has a total of 17 notebooks and 7 pencils)
We now have a system of two equations with two variables. We can solve this system of equations through substitution, elimination, or matrices. Let's solve it using the elimination method:
Multiply Equation 2 by 7 to make the coefficients of p in both equations the same:
7(n + p) = 7(17)
7n + 7p = 119
Now, subtract Equation 1 from the modified Equation 2:
7n + 7p - (18n + 7p) = 119 - 185
7n + 7p - 18n - 7p = -66
-11n = -66
Divide both sides of the equation by -11:
n = -66 / -11
n = 6
Now that we have the value of n (the number of notebooks), we can substitute it back into Equation 2 to find p:
6 + p = 17
p = 17 - 6
p = 11
So, Mr. Smith has 6 notebooks and 11 pencils.
Therefore, Mr. Smith has 6 notebooks and 11 pencils in total.