Find the price of one T-shirt and 1 puck

Question

1 T-shirt and 2 pucks is $36 and two T-shirts’ and 3 pucks is $64.00

Answer 1

In order to solve a problem like this, it is useful to start out by writing down variables which represent the quantities that you are looking for. In this case, let's call t the price of a t-shirt and p the price of a puck.

Then, let's translate these sentences into equations. In particular, you can kind of read these sentences and replace appropriate words with your variables and other mathematical symbols. In this case, you have

1 T-shirt and 2 pucks is $36

which can be translated into

1t + 2p = 36

since "is" can be converted to "equals". You also have the "2 t-shirts and 3 pucks is 64" is the same as 2t + 3p = 64.

You now have two equations

t + 2p = 36

2t + 3p = 64

To solve this system of equations we will eliminate one of the variables as follows. Let's multiply the first equation by -2. This converts our system into

-2t - 4p = -72

2t + 3p = 64

Notice what this does. If we then add these equations together, we will get

(-2t + 2t) + (-4p + 3p) = -72 + 64

0 - p = -8

p = 8.

I multiplied by -2 because I saw that I could then add the equations together and remove one of the variables (in this case t). One I have p = 8, I can solve for t by plugging this value of p into one of my equations. In particular, I have

t + 2p = 36

t + 2(8) = 36

t + 16 = 36

t = 36 - 16

t = 20

Thus my answer to this equation is that a puck costs $8 (because p = 8) and a t-shirt costs $20 because (t = 20).