Marc Buys 4 slices of pizza and 3 soads for $14.50 . Gail buys 2 slices and 2 soads for $8.00. Find the cost of each

Question

Help. me solve this please ......

Answer 1

This is a system of equations problems.

 

We can set up our 2 equations like such,

For Marc: 4p+3s=14.50

For Gail: 2p+2s=8.00

 

We need to solve for one variable, either p or s in either equation.

I will look at Gail because the numbers are smaller and even. Let's solve for s.

 

2s=8-2p

s=4-p

 

Now that we have this lets plug in what we got for s into the first equation (Marc's equation).

4p+3(4-p)=14.5

 

We only have on variable, p, to solve for so it won't be too bad from here.

4p+12-3p=14.5

p+12=14.5

p=2.5

 

And now plugging this back into the second equation,

s=4-(2.5)

s=1.5

 

Therefore, pizza's are $2.50 a slice and sodas are $1.50.

 

Hope this helps!

 

 

Answer 2

This is an example of a system of equations.  Let's call the price of a soda x, and the price of a slice of pizza y.  Each purchase can then be phrased as an equation:

 

4y + 3x = 14.50  (Four slices of pizza plus 3 sodas costs $14.50)

2y + 2x = 8.00  (Two slices of pizza plus two sodas costs $8.00)

 

We can solve the lower equation for y fairly easily:

y + x = 4

y = 4 - x

And then plug this into the upper equation

 

4(4 - x) + 3x = 14.50

16 - 4x + 3x = 14.50

-x = -1.5

x = 1.5

 

The price of a soda is $1.50

 

Take this value for x and plug it into the equation for y obtained earlier:

y = 4 - 1.5

y = 2.5

 

The price of a slice of pizza is $2.50.

 

Check that it works:

4 * $2.50 + 3 * $1.50 = $10 + $4.50 = $14.50

2 * $2.50 + 2 * $1.50 = $5 + $3 = $8

So yes, it works.