1. ms. morton likes to make weird tasting cookies. she decides to make cookies for friends and her
students. each friend will get 3 more cookies than each student. she has a total of 112 students
and 12 friends and made of total of 408 cookies for everyone. the system of equations
represents this scenario:
s y=x+3
(112x +12y = 408
ms. morton predicts that she will give each friend 4 cookies and each student 7 cookies. is she correct?
if not, how many cookies will each friend get and each student get?

Morton will give 3 cookies to each student and 6 cookies to each friend

Solution:

Let "x" be the cookies given to each student

Let "y" be the cookies given to each friend

Each friend will get 3 more cookies than each student

Therefore,

cookies given to each friend = 3 + cookies given to each student

y = x + 3 eqn 1

She has a total of 112 students  and 12 friends and made of total of 408 cookies for everyone

Therefore, we frame a equation as:

112x + 12y = 408 eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

112x + 12(x + 3) = 408

112x + 12x + 36 = 408

124x = 372

x = 3

Substitute x = 3 in eqn 1

y = 3 + 3

y = 6

Thus Morton will give 3 cookies to each student and 6 cookies to each friend

Ms. Morton predicts that she will give each friend 4 cookies and each student 7 cookies. So this is incorrect