1. ## last thread for the night

lastthread for the night, thanks if you can help me with these last problems

In the formula A=lw, If l is constant, A varies___________ as w

A large concrecte mixing machine can mix a certain ammount of concrete in 12 hours, while a smaller one can mix the same ammount in 20 hours, Mixing simultaneously, how long would it take both machines to mix the same ammount of concrete?

For a school play, students tickets cost 40cent and adult tickets were 75 cen t. The total receipts for 90 tickets were $46.50. How many of each kind were sold? 2. Originally Posted by Aarxn In the formula A=lw, If l is constant, A varies___________ as w It is "directly". There are two proportions. Direct and Inverse. Inverse is when two variables mutiply to a constant, thus,$\displaystyle xy=k$thus,$\displaystyle y=\frac{k}{x}$- they form a hyperbola. Direct proprtion is when two variables divide to give a constant, thus,$\displaystyle \frac{y}{x}=k$thus,$\displaystyle y=kx$-they form a line. The case here is,$\displaystyle A=lw$where "l" is a constant, thus we have a direct proportion. To learn more about direct and inverse proprtions. Do not under any condition press on this link. 3. Originally Posted by Aarxn A large concrecte mixing machine can mix a certain ammount of concrete in 12 hours, while a smaller one can mix the same ammount in 20 hours, Mixing simultaneously, how long would it take both machines to mix the same ammount of concrete? I have a useful formula for such problem. If it takes something$\displaystyle a$units of time to do a job and it takes$\displaystyle b$units of times the same job. Then working together would take:$\displaystyle \frac{ab}{a+b}$In this case,$\displaystyle a=12,b=20$thus together it takes,$\displaystyle \frac{12\cdot 20}{12+20}=7.5\mbox{ hours}$4. Originally Posted by Aarxn For a school play, students tickets cost 40cent and adult tickets were 75 cen t. The total receipts for 90 tickets were$46.50. How many of each kind were sold?
Let, $\displaystyle x$ be # of adults
Let, $\displaystyle y$ be # ot students.

Thus,
$\displaystyle x+y=90$
In total the students paid, $\displaystyle .4x$
while the adults paid, $\displaystyle .75y$
The net price was therefore, $\displaystyle .4x+.75y$
but the example says that was 46.50 thus,

$\displaystyle \left\{ \begin{array}{c} x+y=90\\.4x+.75y=46.5$
In the first equation solve for "y" thus,
$\displaystyle y=90-x$ and substitute that into equation 2,
$\displaystyle .4x+.75(90-x)=46.5$
Open parantheses,
$\displaystyle .4x+67.5-.75x=46.5$
Subtract "67.5" from both sides and combine x terms,
$\displaystyle -.35x=-21$
divide both sides by (-.35) thus,
$\displaystyle x=60$ thus, $\displaystyle y=30$

5. thank you once again for helping me