word problem

Question

you bought 15 total tickets for Met opening day. Each upper deck ticket costs $30 and each lower deck ticket costs $45. If you spent $570, how many upper deck and how many lower deck tickets should you buy?

Answer 1

This is a problem with two unknowns, # of upper deck tickets and # of lower deck tickets, so you will need two equations to solve for them.

 Let's let x = # of upper deck tickets

             y = # of lower deck tickets

Eq. I: We know that you bought 15 tickets, so

                                                                    x+y=15

Eq. II: We know that the total cost was $570, so

                                                                   30x+45y=570

You can use the substitution method or elimination method to solve for either x or y. Let's use the substitution method and solve for x. From Eq. I:

                                          x+y=15--->y=15-x

Use this "value" for y in Eq. II to solve for x:

                                                                 30x+45y=570

                                                                 30x+45(15-x)=570

                                                                 30x+675-45x=570

                                                                 -15x+675=570

                                                                 -15x=570-675 

                                                                 -15x=-105

                                                                     x=7

Now, putting this value for x back into Eq. I we can solve for y:

                                                                 x+y=15

                                                                 7+y=15

                                                                 y=15-7

                                                                 y=8

We shall now check that both equations are met with these values:

Eq. I: x+y=15                       Eq. II: 30x+45y=570

         7+8=15                                 30(7)+45(8)=570

          15=15                                  210+360=570

        Check                                         570=570

                                                          Check

Therefore, the answer is that you bought 7 upper deck and 8 lower deck tickets.