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

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

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

Step 2

solve the equations:

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

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

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

and

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

so

$undefined$

c