the school bought a new copy machine which makes 20 copies per minute.the old machine makes 12 copies per minute.francine needs 1000 copies,so she uses both machines.how long will it take to have the copies
solve the following system of equations by first rearranging them so that they are not in fractional form:
3/(x+2) -2/(x+3)=7y/(3x^2+15x+18)
4(y+3) +1/(y+1)= 11x/(Y^2+4y+3)
Easy x=2 and x=3
solve the following system of equations by first rearranging them so that they are not in fractional form:
3/(x+2) -2/(x+3)=7y/(3x^2+15x+18)
4(y+3) +1/(y+1)= 11x/(Y^2+4y+3) oh please help oh please my math teach will funk me if i don't get these problem porrect.
rate of 1st machine = 20 copies/min
rate of 2nd machine = 12 copies/min
combined rate = 32 copies/min
so to make 1000 copies takes
1000/32 or 31.25 minutes or
31 minutes and 15 seconds
Please do not post a new question as an answer to an existing problem, it could easily be considered to be an answer and could thus be ignored.
3/(x+2) -2/(x+3)=7y/(3x^2+15x+18)
3/(x+2) - 2/(x+3) = 7y/(3(x+2)(x+3))
multiplyeach term by 3(x+2)(x+3) , the LCD
9(x+3) - 6(x+2) = 7y
9x + 27 - 6x - 12 = 7y
3x - 7y = -15 -----> #1
Repeat the same thing for the 2nd equation, it works out just as simple
Note that y^2 + 4y + 3 = (y+1)(y+3)
Now you have 2 simple linear equations with x and y, and judging by the complexity of the two starting equations, you obviously know how to do that.
To determine how long it will take to make the copies, we need to find the total number of copies made per minute when both machines are used.
The new machine makes 20 copies per minute and the old machine makes 12 copies per minute. So, the total number of copies made per minute when both machines are used is 20 + 12 = 32 copies per minute.
Francine needs a total of 1000 copies. To find out how long it will take to make these copies, we can divide the total number of copies by the number of copies made per minute:
Time = Total copies / Copies made per minute
Time = 1000 / 32 ≈ 31.25 minutes.
Therefore, it will take approximately 31.25 minutes to make 1000 copies using both machines.