Solve for x and y

Question

Matt sold 3 small boxes and 14 large boxes for a total of $203. Ming sold 11 small boxes and 11 large boxes for a total of $220. Find the cost of 1 small box and 1 large box

Answer 1

Hi Dominic,

Step 1:

Let y= the number of large boxes

Let x = the number of small boxes  

Step 2:

We create a system of equations to evaluate Matt vs. Ming

Matt: 3x+14y=203

Ming: 11x+11y=220

Step 3:

Now we solve the system of equations

(3x+14y=203)(-11) Multiply Matt's entire equation by -11 

(11x+11y=220)(3) Multiply Ming's entire equation by 3

The result of our multiplication is: 

-33x-154y=-2233

33x+33y=660

Now, we continue to solve the equations by combining like terms. Remember, the x terms cancel: 

-121y=-15573 

y=(-1573)/(-121)

y=13

Step 4:

Since we have solved for our y term, we plug this into either of our equations to solve for x.

3x+14(13)=203

3x+182=203

3x=203-182

3x=21

x=7

∴A small box costs $7 while a large box costs $13.

Best, 

Star