Question

Kareem and Bradley are buying school supplies. Kareem spent $42.15 on five notebooks and two packages of pens. Breadly spent $36.35 on threes notebooks and four packages of pens

Answer 1

Let x be price of one notebook and y be price of one package of pen.

The equation for cost of 5 notebooks and two package of pens are,

`5x+2y=42.15`

The equation for cost of three notebook and four package of pens is,

`3x+4y=36.35`

So system of equations for the cost of one notebook and one package of pen is,

5x + 2y = 42.15

3x + 4y = 36.35

PART B

Multiply the equation 5x + 2y = 42.15 by 2 to obtain the same coefficient of y.

`\begin{gathered} 2(5x+2y=42.15) \\ 10x+4y=84.3 \end{gathered}`

Substract equation 3x +4y = 36.35 from equation 10x + 4y = 84.3 to obtain the value of x.

`\begin{gathered} 10x+4y-(3x-4y)=84.3-36.35 \\ 7x=47.95 \\ x=(47.95)/(7) \\ =6.85 \end{gathered}`

Substitute 6.85 for x in equation 3x +4y = 36.35 to obtain the value of y.

`\begin{gathered} 3\cdot6.85+4y=36.35 \\ 4y=36.35-20.55 \\ y=(15.8)/(4) \\ =3.95 \end{gathered}`

The price of a notebook is $6.85 and price of a package of pen is $3.95.