Question

Two factory plants are making TV panels. Yesterday, Plant A produced 2000 fewer panels than Plant B did. Two percent of the panels from Plant A and 5% of thepanels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 660 defective panels?

Answer 1

let x be the amount of panels that plant A produced and y the amount of panels that plant B produced. First we are told that plant A produced 2000 fewer panels tan plant B. This means that if we subtract 2000 from the amount that plant B produced, we would get the amount that plant A produced. This translates to the equation

`y\text{ -2000=x}`

which is equivalent to the equation

`y\text{ -x=2000}`

next, we will calculate the amount of defective panels per plant and then add them up. THis final quantity should be 660. We are told that 2% of plant A's production is defective and that 5% of plant B's production is defective. Recall that to calculate the x% of a number, we simply mulitply the number by x and divide it by 100. So we have that 2% of plant A's production would be

`(2)/(100)x`

and the 5% of plant B's production would be

`(5)/(100)y`

if we add this quantities, we get the equation

`(2)/(100)x+(5)/(100)y=660`

If we multiply both sides by 100, we get the equivalent equation

`2x+5y=66000`

NOw, we want to solve this system of linear equations to find the values of x and y. MOre especifically, we want the value of y. Let us take the first equation, multiply it by 2 and then add it to the second equation, so we get

`2x+5y+2\cdot(y\text{ -x)=66000+2}\cdot2000=70000`

on the left we get

`2x+5y+2y\text{ -2x=7y=664000}`

so, if we divide both sides by 7, we get

`y=(70000)/(7)=10000`

so plant B produced 10000 panels