# word problem equations

• Feb 8th 2008, 02:58 PM
Rocher
word problem equations
I hope you guys can help me... because it's easy but for some reason I can't figure it out? -.-

1) Two hundred people attend a concert. The total receipts are $4500. If one student ticket costs$5, and one adult ticket costs $30, find the number of students who attend the concert? 2) A farmer raises some pigs and chickens. Among the pigs and chickens there are 24 heads and 64 feet. How many pigs and chickens are there? Substitution only please. Come to think of it... maybe you guys can just do one and I can use your steps from the first one to do second :) • Feb 8th 2008, 03:42 PM mathmonster from question 1, u can see that if x is number of student and y is number of adults then 200 = x + y, and so$4500 = $5x +$30y then use the substitution x = 200 - y
and go from there
• Feb 8th 2008, 03:57 PM
OzzMan
Let $x=$the Number of tickets sold

$5x+30x=4500$
$\Rightarrow 35x=4500$
$\Rightarrow x=128.57$ Round up if you like
$(128.57)(5)=642.85$

Roughly 642 students attended the concert assuming my equation is correct.
• Feb 8th 2008, 03:59 PM
mathmonster
OZzman u havent taken into acount the adults also attending!
and it says in total only 200 ppl attended
• Feb 8th 2008, 04:03 PM
OzzMan
Oh yea you're right.
• Feb 8th 2008, 04:10 PM
OzzMan
$4500=5(200-y)+30y$
$4500=1000-5y+30y$
$4500=1000+25y$
$3500=25y$
$y=140$

$200-140=60$
$60$ Students attended
• Feb 8th 2008, 04:22 PM
Rocher
Quote:

Originally Posted by mathmonster
from question 1, u can see that if x is number of student and y is number of adults then 200 = x + y,
and so $4500 =$5x + \$30y then use the substitution x = 200 - y
and go from there

Where did you get 200 from.

• Feb 8th 2008, 04:31 PM
Rocher
Alright, so for question #2, there are 8 pigs and 16 chickens.

Now, can you guys help me with the harder questions? XD

Solve using substitution

1)
x-5y=8
4x+26=10

2)
3x+2y=16
3y-x=13

--

Solve using elimination

1)
2u=3v
u+2v=7

2)
-4x+3y=17
3x-2y=10

--

1) Given two numbers whose difference is 20 such that twice on number equals three times the other. Find the numbers.

Thanks!
• Feb 9th 2008, 01:09 AM
OzzMan
Substitution #2

$3x+2y=16$

$3y-x=13\quad\Rightarrow -x=(13-3y)\quad\Rightarrow x=-13+3y$

$3(-13+3y)+2y=16\quad\Rightarrow -39+9y+2y=16\quad\Rightarrow 11y=55\quad\Rightarrow y=5$

$3(5)-x=13\quad\Rightarrow 15-x=13\quad\Rightarrow -x=-2\quad\Rightarrow x=2$

Elimination #1

$2u=3v\quad\Rightarrow 2u-3v=0$

$u+2v=7\quad\Rightarrow (u+2v=7)-2\quad\Rightarrow -2u-4v=-14$

Now add the equations $2u-3v=0$ and the $-2u-4v=14$ the u's will cross out leaving v as the only variable

$-7v=-14\quad\Rightarrow v=2$

Now plug v back into the original equation to solve for the other variable $u+2(2)=7\quad\Rightarrow u+4=7\quad\Rightarrow u=3$
• Feb 9th 2008, 06:51 AM
Rocher
Can you help me do the other ones too? Because I have looked at them and they are nowhere near similar...

[EDIT] Wait I got the substitution one #2. Now just need elimination and that other question...
• Feb 9th 2008, 06:57 AM
earboth
Quote:

Originally Posted by Rocher
...

1) Given two numbers whose difference is 20 such that twice on number equals three times the other. Find the numbers.

The first number is x
the second number is y.

Then you know: x - y = 20 (from this equation you know that x > y)
and 2x = 3y

Use substitution: y = x - 20

2x = 3(x-20) Expand the bracket and collect like terms, x at the LHS.

-x = -60 that means: x = 60 and therefore y = 40.
• Feb 15th 2008, 05:15 PM
Rocher
Okay thank you now I just need the final question :D