Elizabeth and Lauren sold cookies for a school fundraiser and made $1,316.70. Together the girls sold a total of 831 cookies. Elizabeth sold chocolate chip cookies for $1.50 each, and Lauren sold peanut butter cookies for $1.65 each. How many cookies did Lauren sell?
How would I set this up in order to solve for each?
If they sold x chocolate chips, then
the rest (831-x) were peanut butters
Now just add up the amounts made on each kind.
1.50x + 1.65(831-x) = 1316.70
To set up the problem, let's define two variables:
Let's say that Elizabeth sold x cookies and Lauren sold y cookies.
From the information given in the problem, we know the following:
1. The total amount of money made from selling cookies is $1316.70.
2. The total number of cookies sold is 831.
3. Elizabeth sold chocolate chip cookies for $1.50 each.
4. Lauren sold peanut butter cookies for $1.65 each.
Now, let's use this information to set up two equations:
Equation 1: The total amount of money made from selling cookies
($1.50 * x) + ($1.65 * y) = $1316.70
Equation 2: The total number of cookies sold
x + y = 831
Now, you can solve these two equations simultaneously to find the values of x and y, which will represent the number of cookies sold by Elizabeth and Lauren, respectively.
To solve this problem, you can set up a system of equations based on the given information. Let's use the variables "x" to represent the number of chocolate chip cookies Elizabeth sold, and "y" to represent the number of peanut butter cookies Lauren sold.
We know that the total number of cookies Elizabeth and Lauren sold is 831, so we can write the equation:
x + y = 831 (Equation 1)
We also know the total amount of money they made was $1,316.70, so we can write another equation using the prices of the cookies:
1.50x + 1.65y = 1316.70 (Equation 2)
Now, you have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). You can solve this system of equations to find the values of x and y.
There are various methods to solve the system, such as substitution or elimination. Let's use the substitution method here:
From Equation 1, we can rewrite it as:
x = 831 - y
Now substitute this value of x in Equation 2:
1.50(831 - y) + 1.65y = 1316.70
Simplify and solve the equation to find the value of y. Once you find the value of y, you can substitute it back into Equation 1 to calculate the value of x.