a courier company charges $3 for every package delivered safely and pays back $5 for every package lost. If the company was paid 320 for 120 packages, how many packages did the company lose?
X delivered safely.
Y lost.
Eq1: x+y = 120.
Eq2: 3x - 5y = $320.
Multiply Eq1 by 5 and add the Eqs:
5x + 5y = 600
3x - 5y = 320
sum: 8x = 920
X = 115.
In Eq1, replace X with 115 and solve for Y.
d + L = 120
3 d + 5 L = 320
solve the system for L
To find the number of packages lost by the courier company, we can set up an equation based on the given information.
Let's assume that the number of packages lost is "x".
According to the given information, the courier company charges $3 for every package delivered safely and pays back $5 for every package lost.
So, the revenue earned by the courier company for the packages delivered safely would be 120 (total number of packages - x) multiplied by $3, which can be written as 3(120 - x).
The amount paid back by the company for the lost packages would be "x" (the number of lost packages) multiplied by $5, which can be written as 5x.
Given that the company was paid $320 in total, we can set up the equation:
3(120 - x) + 5x = 320
Now, we can solve this equation to find the value of "x" (the number of packages lost).
Expanding the equation:
360 - 3x + 5x = 320
Combining like terms:
2x + 360 = 320
Subtracting 360 from both sides:
2x = 320 - 360
2x = -40
Dividing both sides by 2:
x = -40/2
x = -20
Since "x" represents the number of packages lost, we cannot have a negative number of lost packages. Therefore, the negative solution is not valid in this context.
Hence, the courier company did not lose any packages.