Morgan paid $15.50 for 5 slices of pizza and 2 drinks. Pat got 8 slices of pizza and 4 drinks for $26.00. How much would an order of 2 slices of pizza and 2 drinks cost?

Answer 1

For this problem, they're providing you with two equations - just in text form rather than equation form. Your first step to solving this is converting it to equations:

"Morgan paid $15.50 for 5 slices of pizza and 2 drinks"

This, in equation form, is:

5p + 2d = $15.50 (where p stands for the unknown pizza cost and d stands for the unknown drink cost. You can use whatever variables you like, for instance many equations use x and y, but I use variables which help me identify what they represent. You could use whatever you want though, they're just placeholders for unknown values.)

"Pat got 8 slices of pizza and 4 drinks for $26.00"

In equation form, this is:

8p + 4d = $26.00

Now, you can solve this one of two ways. You can either isolate a variable in one of the equations then solve for the other - or you can subtract the equations from each other. I'll cover both below:

Method 1: Isolate Variable

First, pick an equation and a variable within that equation to isolate. It doesn't matter which equation or which variable, this work with whichever you choose. I'll use the second equation and solve for d, the cost of a drink. (Note: we won't get the numerical cost just yet, but we'll get there eventually.)

8p + 4d = 26.00 (First, isolate 4d by getting rid of 8p on the left side of the equation. To do this, since the left side of the equation is adding 8p, we want to subtract 8p from both sides. This allows us to cancel the 4d on the left side but keeps the equation equal on both sides of the equal sign. For instance, if we had an equation with 82 + 14 = 96, both sides are currently equal. If we wanted to "get rid" of the 14 on the left side and only subtracted 14 from the left side, we'd be left with 82 + 14 - 14 = 96 which isn't accurate anymore. We'd have to also subtract 14 from the right side... 82 + 14 - 14 = 96 - 14. When you simplify this, you end up with 82=82 which is still accurate.)

8p + 4d - 8p = 26.00 - 8p (we can cancel out the 8p - 8p on the left side, as anything minus itself is 0 and we don't need to write "+0" on an equation)

4d = 26.00 - 8p (Next, we need to finish getting the d variable by itself; it still has a 4 that it's being multiplied by on the left side. Just like we subtracted to cancel out adding 8p to the left side, we have to do the opposite of multiplying by 4 to cancel it out. Just remember to do this to both sides!)

4d/4 = (26.00 - 8p)/4 (simplify, including separating the fraction and simplifying individually... also, you can cancel out 4/4 on the left, as that equals 1 and 1 times any number is that number)

d = 26.00/4 - 8p/4

d= 26/4 - 2p (simplify)

d = 13/2 - 2p

Now we have an equation that gives us what the cost of a drink is... as long as we know what the cost of a pizza is. That may not seem very helpful, but it's exactly what we need. We can now plug this new equation we created into the other equation (the 1st equation, because I used the 2nd to get the d= 13/2 - 2p equation) and simplify it. Since we know that d=13/2 - 2p, the following two equations are equal:

5p + 2d = $15.50

5p + 2(13/2 - 2p) = $15.50

So we just simplify the lower version then solve for p.

5p + (26/2 - 4p) = $15.50

5p + 13 - 4p = $15.50

p + 13 =$15.50

p = $2.50

So the cost of a pizza is $2.50. Well, we already know what the cost of a drink is as long as knew what the cost of a pizza was. Now we know what a pizza costs! Let's use our equation from earlier:

d = 13/2 - 2p

d = 13/2 - 2(2.50)

d = 13/2 - 5 (convert fraction to a decimal)

d = 6.5 - 5

d = 1.5 (or $1.50)

So a drink is $1.50 and a pizza costs $2.50. The easier method to solve this, though is to:

Method 2: Subtract Equations

As long as the two equations have the same terms and form, we can just subtract one equation from the other. See below where I've taken the two equations and lined them up based on like-terms.

5p + 2d = 15.50

8p + 4d = 26.00

We could subtract the lower equation from the upper equation, but that doesn't really get us anywhere. We still have two variables to solve for. The goal with subtracting equations is to get one of the variables to disappear. That being said, we can still make that happen here!

Notice how the 2nd equation has a d value that's twice as much as the d value in the upper equation? Well, we could divide that 4d in half - as long as do that exact same mathematical operation to all values in the equation.

8p + 4d = 26.00 (divide everything by 2)

4d + 2d = 13.00

Now, let's line up the equations and subtract like terms.

5p + 2d = 15.50

- 4p + 2d = 13.00

_______________

1p + 0d = 2.50 (or, in simple terms, p + 0 = 2.50, or p = 2.50)

Now, just plug this value into either equation then solve for d!

How much would the new order cost?

Finally, the question asks how much an order of 2 slices of pizza and 2 drinks cost. This is a new equation:

2p + 2d = ?

Well, we have the value for p and the value for d. Just solve for this new value!