Algebra problem

• Sep 29th 2008, 03:45 PM
Neenoon
Algebra problem
Here is the statement: Many people are sharing a bill. The payment would have been 40cents less per person if they had been 10 people more. In reverse, they would have pay 50 cents more per person if they had been 5 people less. What is the x number of person? And what amount would they each pay?

Here is what I did:

What I'm looking for:
1. the number of person, x
2. the amount each paid, y
3. the bill amount, xy

What I know:
- the bill would have been 0.40\$ less per person if they had been 10 person more. (y-0.40) (x+10) = xy
- the bille would have been 0.50\$ more if they had been 5 person less.
(y+0.50) (x-5) = xy

I can simplify both of these:

(y-0.40) (x+10) xy
xy+10y-10x-4=xy
10y-0.40x=4

(y+0.50) (x-5) = xy
xy-5y+0.50x-2.5 = xy
0.50x-5y=2.5 or x-10y=5

-0.40x+10y=4
+ x-10y = 5
---------------
0.6x = 9
x = 15

Replacing x and finding y:

(y+0.50) (15-5) = 15y
15y-5y+7.5-2.5 = 15y
-5y = -5
y = 1

So, I get that there are 15 people and they each paid 1\$

Is there something wrong in this?
• Sep 29th 2008, 03:50 PM
Neenoon
HW3-Qst 10 : parenthesis and [] use in equations
I'm writing this:

4018.60+(0.07x4018.60)+[((0.07x4018.60)+4018.60)0.075]=4622.40

I want this the third part to be done in this order:

(0.07x4018.60) = 281.302
+4018.60 = 4299.902
x 0.075 = 322.49265

So that the calculation should be:

4018.60 + 281.302 + 322.49265 = 4622.39465

Would someone do it that way, with the () and [] that I used?
• Sep 29th 2008, 06:24 PM
ticbol
Quote:

Originally Posted by Neenoon
Here is the statement: Many people are sharing a bill. The payment would have been 40cents less per person if they had been 10 people more. In reverse, they would have pay 50 cents more per person if they had been 5 people less. What is the x number of person? And what amount would they each pay?

Here is what I did:

What I'm looking for:
1. the number of person, x
2. the amount each paid, y
3. the bill amount, xy

What I know:
- the bill would have been 0.40\$ less per person if they had been 10 person more. (y-0.40) (x+10) = xy
- the bille would have been 0.50\$ more if they had been 5 person less.
(y+0.50) (x-5) = xy

I can simplify both of these:

(y-0.40) (x+10) xy
xy+10y-10x-4=xy
10y-0.40x=4

(y+0.50) (x-5) = xy
xy-5y+0.50x-2.5 = xy
0.50x-5y=2.5 or x-10y=5

-0.40x+10y=4
+ x-10y = 5
---------------
0.6x = 9
x = 15

Replacing x and finding y:

(y+0.50) (15-5) = 15y
15y-5y+7.5-2.5 = 15y
-5y = -5
y = 1

So, I get that there are 15 people and they each paid 1\$

Is there something wrong in this?

None.

If you want to be sure, check back your answers against the original equations.
• Sep 29th 2008, 06:33 PM
ticbol
Quote:

Originally Posted by Neenoon
I'm writing this:

4018.60+(0.07x4018.60)+[((0.07x4018.60)+4018.60)0.075]=4622.40

I want this the third part to be done in this order:

(0.07x4018.60) = 281.302
+4018.60 = 4299.902
x 0.075 = 322.49265

So that the calculation should be:

4018.60 + 281.302 + 322.49265 = 4622.39465

Would someone do it that way, with the () and [] that I used?

I might do it differently, but yours is okay.

The checkers, or the people checking your solution, might get lost at your
(0.07x4018.60) = 281.302
+4018.60 = 4299.902
x 0.075 = 322.49265

but if no one is to check your computations, then you did it fine.

Maybe you could have written the above like this;
(0.07x4018.60) = 281.302

281.302 +4018.60 = 4299.902
4299.902 * 0.075 = 322.49265

I always believe in whatever ways a solution goes as long as the solver understands himself and his solution such that he can review for mistakes in his "unique" solution if necessary.
• Sep 30th 2008, 06:18 AM
Neenoon
My question really is, is the notation correct?

Will this: 4018.60+(0.07x4018.60)+[((0.07x4018.60)+4018.60)0.075]

Thank you so much for looking at this for me.
• Sep 30th 2008, 02:14 PM
ticbol
Quote:

Originally Posted by Neenoon
My question really is, is the notation correct?

Will this: 4018.60+(0.07x4018.60)+[((0.07x4018.60)+4018.60)0.075]

Thank you so much for looking at this for me.