2 cans of paint and 1 roller for $30 bought 3 more cans and 2 more rollers for $50. How much did 1roller cost?

To paint his house, Samuel bought 2 cans of paint and one roller for $30. When friends came over to help, he went back to the store and bought three more cans of paint and two more rollers for $50. How much did he pay for a roller?





dollars per roller =?2 cans of paint and 1 roller for $30 bought 3 more cans and 2 more rollers for $50. How much did 1roller cost?
This is a simultaneous equation so...





let cans of paint be x


and


rollers be y





2x+y=$30 (equation 1)


3x+2y=$50 (equation 2)





(take equation 1 from equation 2)





x+y=$20





so roller=$102 cans of paint and 1 roller for $30 bought 3 more cans and 2 more rollers for $50. How much did 1roller cost?
Set up two equations, one representing his first purchase and a second representing the last purchase. Let the cost of a can of paint be x and the cost of a roller be y. Then these are the two equations to write:





1st Purchase: 2x + y = 30


2nd Purchase: 3x + 2y = 50





There are two ways to solve this. Either use the elimination method, where you multiply one or both equations by a factor and then add or subtract the two equations to eliminate one of the variables, or write one of the variables in terms of the other and solve for the other variable. In this case, it will be easier to do the latter:





2x + y = 30 -----%26gt; y = 30 - 2x.





Now we can plug the value for y into the second equation and solve for x:





3x + 2y = 50


3x + 2 (30 - 2x) = 50


3x + 60 - 4x = 50


3x - 4x = 50 - 60


-x = -10


x = 10





So the cost of a can of paint is $10.





Now that we know the cost of a can of paint, we can solve for the cost of a roller:





2x + y = 30


2 ($10) + y = $30


$20 + y = $30


y = $30 - $20


y = $10





The cost of a roller is also $10.





To verify this is the correct price for a roller, substitute the price for both the paint and the roller into one or both of the equations to see if a true statement results.
he paid $10 per roller..





10+10=2 cans of paint + 10= 1 roller= $30





10+10+10= 3 cans of paint + 10+10= 2 rollers = $50
10 $





2x+y=30


3x+2y=50





-2(2x+y)=30


3x+2y=50





-4x-2y=-60


3x+2y=50





-x=-10





x=10