Q. 58 - Precalculus Enhanced with Graphing Utilities

Question

A movie theater charges \(9.00 for adults and \)7.00 for senior citizens. On a day when 325 people paid an admission, the total receipts were $2495. How many who paid were adults? How many were seniors?

Step-by-Step Solution

Answer

The number of adult is 110 and number of senior citizen is 215

Step 1: Given information

A movie theater charges $9.00 for adults and $7.00 for senior citizens. On a day when 325 people paid an admission, the total receipts were $2495. 

Step 2: Find the equation and solve them

Let the number of adults be x and number of senior citizen be y

Total number of people are 325

hence $x+y=325 \left(1\right)$

Now A movie theater charges $9.00 for adults and $7.00 for senior citizens And the total collection were $2495

hence we get, $9x+7y=2495 \left(2\right)$

Multiply equation 1 by 7 and subtract from equation 2 we get,

$$\begin{gathered} 7(x+y=325) \\ 7x+7y=2275 \left(3\right) \end{gathered}$$

Now we subtract

$9x+7y=2495+-7x-7y=-22752x=220$

hence $x=110$

Also 

$$\begin{gathered} x+y=325 \\ 110+y=325 \\ y=215 \end{gathered}$$

Step 3: Conclusion

The number of adult is 110 and number of senior citizen is 215