Question

There were 676 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper reserved tickets cost $8.00. The total amountof money spent was $6974.00. How many of each kind of ticket were purchased?How many lower box tickets were purchased?How many upper reserved tickets were purchased?

Answer 1

348 lower box

328 upper reserved

1) Considering that there were 676 tickets from 2 kinds, then we can write out:

x+y=676 This equation refers to the quantity

12.5x+8y= 6794 This equation refers to the cost

We are going to call the lower box (x) and the upper reserved (y)

2) So now let's solve this system:

`\begin{gathered} x+y=676 \\ 12.5x+8y=6974 \end{gathered}`

Let's use the Elimination Method, multiplying the first equation by -8:

`\begin{gathered} -8x-8y=-5408 \\ 12.5x+8y=6974 \\ ------------- \\ 4.5x=1566 \\ (4.5x)/(4.5)=(1566)/(4.5) \\ x=348 \end{gathered}`

2.2) We can now find the y value, by plugging it into the first original equation:

348+y=676

y=676-348

y=328

Hence, the answer is:

348 lower box

328 upper reserved

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