SOLUTION: Hello E-Tutors:) Could someone lead me in the right direction with this college system of equations and inequality problem? The text book shows how to solve something simil

Question 150714: Hello E-Tutors:)

Could someone lead me in the right direction with this college
system of equations and inequality problem? The text book shows
how to solve something similiar but it only displays an equation
with two variables. Whereas this problem contains three variables.
That throws me for a loop.

Problem: The students from algebra class go for coffee together
every day. On Monday, Jordan paid $5.45 for three cartons of milk,
four cups of coffee, and seven doughnuts. On Tuesday, Ryan paid $5.30
for four milks, two coffees, and eight doughnuts. On Wednesday, Zack
paid $5.15 for two milks, five coffees, and six doughnuts.

1. Set up a system of equations to model this scenario.

I think this is right, but have no idea how to solve three layers,
with 3 different variables.
m=milk
c=coffee
d=doughnut

3m + 4c + 7d = 5.45
4m + 2c + 8d = 5.30
2m + 5c + 6d = 5.15

2. Determine the cost of one carton milk, one coffee, and one doughnut
by solving they system.

3. If on Thursday, Taylor had to pay for five milks, two coffees, and nine
doughnuts how much did he spend?

Think, I can get this one if I learn how to solve the second question.

Thank you in advance for sharing your valuable skills with us,
mishap mathematicians. :0)

Grateful,
Jai

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
3m + 4c + 7d = 5.45
4m + 2c + 8d = 5.30
2m + 5c + 6d = 5.15
-------------------------
subtract 3rd equation from 1st to get:
m - c + d = 0.30
4m + 2c + 8d = 5.30
2m + 5c + 6d = 5.15
-----------------------
subtract 4 times 1st from 2nd;
subtract 2 times 1st from 3rd:
m - c + d = 0.30
0 + 6c + 4d = 4.10
0 + 7c + 4d = 4.55
----------------------
interchange 2nd and 3rd to get:
m - c + d = 0.30
0 + 7c + 4d = 4.55
0 + 6c + 4d = 4.10
------------------------
subtract 3rd from 2nd to get:
m - c + d = 0.30
0 + c + 0 = 0.45
0 + 6c + 4d = 4.10
----------------------
At this point you can see that c = 0.45
-------------
Subtitute that into the 3rd equation to solve for "d":
6(0.45) + 4d = 4.10
2.7 + 4d = 4.10
4d = 1.40
d = 0.35
----------------
Substitute the values of c and d into the 1st equation to solve for "m":
m - 0.45 + 0.35 = 0.30
m - 0.10 = 0.30
m = 0.40
-----------------
one mild costs 40 cents
one coffee costs 45 cents
one doughnut costs 35 cents
============================
Cheers,
Stan H.

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