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=$50" "...........Equation(2)$
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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 "$10$