Question

2 pens and 1 copybook cost $16.50. 4 pens and 5 copybooks cost $52.50. Neil purchased 2 pens, 2 copy books and 3 rulers and paid $41. Calculate the cost of 1 ruler.

Answer 1

Step-by-step explanation

Step 1

set the equations:

Let x represents the cost of 1 pen

Let y represents the cost of 1 copybook

Let z represents the cost of 1 ruler

so

a)2 pens and 1 copybook cost $16.50

`2x+1y=16.50\rightarrow equation(1)`

b)4 pens and 5 copybooks cost $52.50

`4x+5y=52.50\rightarrow equation(2)`

c) 2 copy books and 3 rulers and paid $41

`\begin{gathered} 2y+3z=41 \\ \text{isolate z value} \\ 3z=41-2y \\ z=(41-2y)/(3)\rightarrow equation(3) \end{gathered}`

Step 2

solve the equations:

`\begin{gathered} 2x+1y=16.50\rightarrow equation(1) \\ 4x+5y=52.50\rightarrow equation(2) \\ z=(41-2y)/(3)\rightarrow equation(3) \end{gathered}`

a) isolate the x value in equation (1) and (2) then set equal each other,

`\begin{gathered} 2x+1y=16.50\rightarrow equation(1) \\ 2x=16.50-y \\ x=(16.50-y)/(2) \end{gathered}`

and

`\begin{gathered} 4x+5y=52.50\rightarrow equation(2) \\ 4x=52.50-5y \\ x=(52.50-5y)/(4) \end{gathered}`

so

c