Maggie made some cookies for her friends. If she gave each friend 7
cookles, she would need another 18 cookies. If she gave each friend
10 cookies, she would need another 66 cookies,
(a) How many friends did Maggie have?
(b) How many cookies did she make?
Number of friends ---- x
number of cookies --- c
c = 7x + 18
c = 10x + 66
subtract:
0 = 3x + 48
x = a negative number
The wording is confusing.
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To determine the number of friends Maggie has, we need to first set up a system of equations based on the given information.
Let's say Maggie has 'x' friends and she made 'y' cookies.
According to the first statement, if Maggie gave each friend 7 cookies, she would need another 18 cookies. This can be written as:
7x = y + 18 --------- (equation 1)
Similarly, according to the second statement, if Maggie gave each friend 10 cookies, she would need another 66 cookies. This can be written as:
10x = y + 66 --------- (equation 2)
Now we can solve this system of equations to find the values of x (number of friends) and y (number of cookies).
To do that, we can use the method of substitution. We'll solve equation 1 for y and substitute it into equation 2.
From equation 1, we have y = 7x - 18.
Substituting this into equation 2, we get:
10x = (7x - 18) + 66
10x = 7x + 48
Simplifying the equation, we have:
10x - 7x = 48
3x = 48
Dividing both sides by 3, we get:
x = 16
Therefore, Maggie has 16 friends.
To find the number of cookies she made, we can substitute this value of x back into equation 1 or 2.
Using equation 1, we have:
y = 7x - 18
y = 7(16) - 18
y = 112 - 18
y = 94
Therefore, Maggie made 94 cookies.
So, the answers to the questions are:
(a) Maggie has 16 friends.
(b) Maggie made 94 cookies.