Together, two printers can print 7500 lines if the first printer prints for 2 minutes and the second prints for 1 minute. If the first printer prints for 1 minute and the second prints for 2 minutes, they can print 9000 lines together. Find the number of lines per minute that each printer prints.
Equation 1: 2*F+S=7500
Equation 2: F+2*S=9000
I am not sure how to solve. Please help. Thank you
Again, this is algebra 2.
printdone= rate*time
1)7500=(rate1+Rate2)2+ rate2*1
2)9000=rate1*1 + rate2*2
You have two equations, two unknowns. Solve for rate2, rate1
To solve this system of equations, we can use the method of substitution. Let's start by solving Equation 1 for F (lines printed per minute by the first printer):
Equation 1: 2F + S = 7500
Rearranging the equation, we have:
2F = 7500 - S
Dividing both sides by 2, we get:
F = (7500 - S) / 2
Now, we can substitute this expression for F into Equation 2:
Equation 2: F + 2S = 9000
Replacing F with (7500 - S) / 2, we have:
(7500 - S) / 2 + 2S = 9000
To simplify, we can multiply both sides by 2 to clear the fraction:
7500 - S + 4S = 18000
Combining like terms, we get:
3S = 10500
Dividing both sides by 3, we find:
S = 3500
Now that we have the value of S, we can substitute it back into Equation 1 to find F:
2F + S = 7500
2F + 3500 = 7500
Subtracting 3500 from both sides:
2F = 4000
Dividing both sides by 2, we get:
F = 2000
Therefore, the first printer prints 2000 lines per minute, and the second printer prints 3500 lines per minute.