Math Help - last thread for the night

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, $xy=k$ thus, $y=\frac{k}{x}$- they form a hyperbola. Direct proprtion is when two variables divide to give a constant, thus, $\frac{y}{x}=k$ thus, $y=kx$-they form a line. The case here is, $A=lw$ 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 $a$ units of time to do a job and it takes $b$ units of times the same job. Then working together would take: $\frac{ab}{a+b}$ In this case, $a=12,b=20$ thus together it takes, $\frac{12\cdot 20}{12+20}=7.5\mbox{ hours}$ 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, $x$ be # of adults
Let, $y$ be # ot students.

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

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

5. thank you once again for helping me