write the equation for the second sentence of this problems

Question

to paint his house Samuel bought two 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 2 more rollers for $50. how much did he pay for a roller

Answer 1

Let C be the cost for a can paint

Let R be the cost per roller

 

Translate the words into variables and operations:

     Two cans of paint and one roller for $30

         2*C + 1*R = 30

 

     Three cans of paint and two rollers for $50

        3*C + 2*R = 50

 

We want to find R (price of rollers), eliminate C by multiplying the first equation by 2 and the sedond equation by 3, then subtracting the first equation from the second equation (to keep R positive on the left side)

      6C + 3R = 90

      6C + 4R = 100

So,

       0  + R  = 10       (R = 10answer)

 

And 2C + 10 = 30   (first equation)

         2C = 20

          C = 10

 

Checking:

     Does 2(10) + 10 = 20    (first equation)   yes

      Does 3(10) + 2(10) = 50    (second equation)   yes

Answer 2

To solve this problem we need two equations. Let cans of paint be c and rollers be r. From the first statement. Samuel bought 2 cans of paint + 1 roller for $30 or simply 2c + 1r = 30. This will be our equation one. He went  back to the store and bought 3 cans of paint + 2 rollers for $50 or simply 3c + 2r = 50. That gives us two equations. Which brings is to what we all love to do. Quadratic equation lol.  since eq. 1 has smaller numbers, sp we can easily isolate r. From eqtion 1.  1r = 30 - 2c or r = 30 - 2c. We can substitute this value of r in eq 2. Which means anywhere we see r in eq. 2, we put (30-2c) instead. That will give us 3c + 2(30-2c) = 50. Let's call this eq 3. We can now easily solve for c since c is the only letter in eq 3. therefore 3c + 60 - 4c = 50. Bringing like terms together, we get 60-50 = 4c - 3c. Remember signs change when they cross the = sign. That makes it 10 = c or c = $10 this is the cost of a can of paint. But we need the cost of a roller.  Since we know the value of c, we can Easily get r by substituting c in the simpler equation which is eq 1. This gives us 2(10) + r = 30. This gives us 20 + r = 30. Therefore r = 30 - 20   Which is also 10.  So he paid $10 for the roller. And also $10 for a can of paint. I hope this helps