A bunch of friends went to the Snack Shack for lunch. The first family ordered 4 hamburgers and 4 orders of fries for $9.00. The next family ordered only 1 hamburger and 2 orders of fries for $3. How much would each item cost individually?

Let hamburgers be h.
Let fries be f

Condition 1:

#4h+4f=$9# ........................(1)

Condition 2:

#h+2f = $3#......................(2)

To eliminate h multiply equation (2) by 4 and then subtract it from (1) leaving only the amount of f and its cost:

#4h+4f=$9 ........................(1)#
#4h+8f=$12 .......................(2_a)#

#(2_a)-(1)# is a better way round that originally intended!

#4f=$3#
#f= 3/4$#...........................(3)
Substitute (3) back into (1) to find h.

I will let you do that bit!

I will answer this question using a system of equations.

The first equation I will make is #4h + 4f = 9#, where #h# is for hamburgers and #f# is for fries.

The second equation I can make based on the given information is #1h + 2f = 3# where, also, #h# is for hamburgers and #f# is for fries. I can modify this equation using the subtraction property of equality. I can subtract #2f# from each side to get #h# on its own. So our equation is now #h = 3 - 2f#.

From equation 2, we have what #h# is equal to. We can plug this into the first equation. #4(3-2f) + 4f = 9#. By following the steps, we can find that #f = 0.75#. Since above we stated that #f# is the variable for fries, it is $0.75 for fries.

Now that we have #f#, we can plug it into our #h=3-2f# equation. That would look like this: #h = 3- 2(0.75)#. When you solve this equation, you get #h = 1.5#. Since we stated that #h# is the variable for hamburgers, it is $1.50 for hamburgers.

Using the question "A bunch of friends went to the Snack Shack for lunch. The first family ordered 4 hamburgers and 4 orders of fries for $9. The next family ordered only 1 hamburger and 2 orders of fries for $3. How much would each item cost individually?" We can set up the varible #h# for hamburgers and #f# for fries.

Next we would set up equations. Since family one has 4 hamburgers and 4 fries for $9 we can put that into the equation #4h+4f=9#.
We do the same thing for family two with 1 hamburger, 2 fries, and $3 to get the equation #(1)h+2f=3#.

Now we need to take either equation and simplify it to equal a variable. Since the second equation is simpler, I'm going to use that one. The step by step simplification of equation 2 is:
#h+2f=3#
#h=3-2f#
since we now know the value of #h# we plug that into #4h+4f=9# to turn it into #4(3-2f)+4f=9#.
The step by step silification:
#4(3-2f)+4f=9#
#12-8f+4f=9#
#12-4f=9#
#-4f=-3#
#f= (-3)/-4# which is the same as #f= 3/4#. This mean fries cost 3/4 of a dollar which is $0.75.

Now putting the value of #f# (which is #3/4#) into the equation #h=3-2f# we solve for the value of #h#.
Step by step:
#h=3-2(3/4)#
#h=3-1 1/2#
#h=1 1/2#
so #h# is one and a half dollars which is the sames as $1.50.

So your answer is...
A Hamburger costs $1.50
An Order of Fries costs $0.75.

The thing we did when we plugged in one value for another is called the substitution property and is an awesome way to find answers to algebraic equations like these. The substitution property is when you take one value and plug it in for a equal value in another equation, and that's what we did to find your answer.

I hope this helps, Good Luck!