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?

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Answer 1 · 2017-05-21T14:53:52

#"1 can of paint costs "$10.00#
#"1 roller costs "$10#

Let the price of a can of paint be #c#
Let the price of a roller be #r#

Condition 1#->2c+1r=$30" ".............Equation(1)#
Condition 2#->3c+2r=$50" "...........Equation(2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Multiply everything in #Equation(1)# by 2 giving:

#4c+2r=$60" ".............Equation(1_a)#
#3c+2r=$50" "...........Equation(2)#

#Equation(1_a) - Equation(2)#

#c+0=$10=>" 1 can of paint costs "$10.00#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider equation(2). I can costs $10 so we have:

#3(10)+2r=$50#

#$30+2r=$50#

Subtract $30 from both sides

#0+2r=$20#

Divide both sides by 2

#r=$10 =>" 1 roller costs "$10#