Answer:
3. 314 student and 226 adult
4. x = 6.5, y = -0.5
Step-by-step explanation:
3. First we will take our information and make a system of equations:
[tex]2.4a+1.25s=934.9[/tex]
[tex]a+s=540[/tex]
[tex]a[/tex] is the number of adult tickets sold and [tex]s[/tex] is the number of student tickets sold.
From the second equation we can rearange it to be:
[tex]a=540-s[/tex]
Then we can plug in our new value of [tex]a[/tex] to our first equation
[tex]2.4(540-s)+1.25s=934.9[/tex]
[tex]1296-2.4s+1.25s=934.9[/tex]
[tex]1.15s=361.1[/tex]
[tex]s=314[/tex]
We can then find [tex]a[/tex] by plugging in s to our second equation
[tex]a+314=540[/tex]
[tex]a=226[/tex]
4. It is mostly solved already. We can take the value of y from the first equation and plug it into the second to get:
[tex]3x -5(-5x+32)=22[/tex]
[tex]3x+25x-160=22[/tex]
[tex]28x=182[/tex]
[tex]x=6.5[/tex]
Then plug our value of x into the first equation to get:
[tex]3(6.5)-5y=22[/tex]
[tex]19.5-5y=22[/tex]
[tex]5y=-2.5[/tex]
[tex]y=-0.5[/tex]
