mr yang daily wage was $5 more than mr chen. Although mr yang worked 3 days lss than mr chen, they earn $180 each. find number of days mr yang worked.
Ah, let me put on my working clown nose for this math problem!
So, let's assume that Mr. Chen worked for 'x' days. That means Mr. Yang worked for 'x - 3' days because he worked 3 days less.
Now we know that Mr. Yang earned $5 more per day than Mr. Chen. So if Mr. Chen earned 'y' dollars per day, Mr. Yang earned 'y + 5' dollars per day.
Since they both earned $180, we can set up an equation:
(x)(y) = (x - 3)(y + 5)
Simplifying this equation, we get:
xy = xy + 5x - 3y -15
Now, let's cancel out the 'xy' terms:
0 = 5x - 3y - 15
Moving things around a bit:
-5x + 3y = 15
Hmm... it seems we don't have enough information to find the exact number of days Mr. Yang worked. Can we assume the wage rates for Mr. Chen and Mr. Yang?
Let's solve this step by step:
1. Let's assume Mr. Chen's daily wage as "x".
2. According to the given information, Mr. Yang's daily wage is $5 more than Mr. Chen's daily wage. So, Mr. Yang's daily wage would be "x + $5".
3. Let's assume Mr. Chen worked for "y" number of days.
4. According to the given information, Mr. Yang worked 3 days less than Mr. Chen. So, Mr. Yang worked for "y - 3" number of days.
5. Now, we can calculate the earnings of Mr. Chen and Mr. Yang.
- Mr. Chen's earnings: x * y
- Mr. Yang's earnings: (x + $5) * (y - 3)
6. According to the given information, both Mr. Chen and Mr. Yang earned $180 each. So, we can form an equation based on their earnings:
- x * y = $180
- (x + $5) * (y - 3) = $180
7. Let's solve these equations simultaneously to find the values of x and y.
It seems that there are not enough equations to solve for the exact values of x and y.
To solve this problem, let's assign variables to the unknown quantities:
Let x be the number of days Mr. Chen worked.
Let y be Mr. Yang's daily wage.
We are given the following information:
Mr. Yang earned $5 more than Mr. Chen's daily wage, which means y = (y - $5).
Even though Mr. Yang worked 3 days less than Mr. Chen, both of them earned $180.
Using this information, we can set up two equations:
1. The equation for their daily wages:
y - 5 = x
2. The equation for their total earnings:
y * (x - 3) + x * y = 180
Now, let's solve the equations simultaneously:
Substitute the first equation into the second equation:
(y - 5) * (x - 3) + x * y = 180
Expand the equation:
yx - 5x - 3y + 15 + xy = 180
Combine like terms:
2xy - 5x - 3y + 15 = 180
Rearrange the equation:
2xy - 3y - 5x = 165
Now, let's try different values of x to find the solution:
We start with x = 1:
2y - 3y - 5 = 165
-y - 5 = 165
-y = 170
(y = -170)
Since we cannot have a negative value for the daily wage, this solution is not feasible.
Let's now try x = 2:
2y - 3y - 10 = 165
-y - 10 = 165
-y = 175
(y = -175)
Again, this solution is not feasible.
Let's now try x = 3:
2y - 3y - 15 = 165
-y - 15 = 165
-y = 180
(y = -180)
This solution is also not feasible.
Finally, let's try x = 4:
2y - 3y - 20 = 165
-y - 20 = 165
-y = 185
(y = -185)
Once again, this solution is not feasible.
Since we have exhausted all possible values of x, we can conclude that there are no valid solutions to this problem.
y=c+5
If chen worked x days,
y(x-3) = 180
cx = 180
I get x=12, so yang worked 9 days.