Chapter 6, Problem 19PT

To determine

To write a system of equations to represent the situation and solve.

Answer to Problem 19PT

Cost of one ream of paper: $7.5

Cost of one inkjet cartridge: $35

Explanation of Solution

Given:

Ricardo bought 24 reams of paper and 4 inkjet cartridges for $320.

Britney bought 2 reams of paper and 1 inkjet cartridge for $50.

The price of the reams of paper is same and the inkjet cartridges were all the same price.

Concept used:

Assume separate variables for each object. Form two equations with the variables. Use elimination method and solve the system of equations.

Calculation:

Let x be the cost of one ream of paper and y be the cost of one inkjet cartridge.

Richard has bought 24 reams of paper and 4 inkjet cartridges for $320.

  $\Rightarrow 24x+4y=320$ ……………… (1)

Britney has bought 2 reams of paper and 1 inkjet cartridges for $50.

  $\Rightarrow 2x+y=50$ …………………… (2)

Solve the system of equations (1) and (2)

Multiplying (2) with 12,

  $\Rightarrow 24x+12y=600$ ………….. (3)

Subtracting (2) from (3),

  $\begin{array}{l}24x+12y=600\\ \frac{-24x-4y=-320}{8y=280}\end{array}$

Dividing 8 on both sides,

  $\begin{array}{c}\frac{8y}{8}=\frac{280}{8}\\ y=35\end{array}$

Substituting the value of y in (2),

  $2x+35=50$

Subtracting 35 on both sides,

  $\begin{array}{l}2x+35-35=50-35\\ 2x=15\end{array}$

Dividing 2 on both sides,

  $\begin{array}{c}\frac{2x}{2}=\frac{15}{2}\\ x=7.5\end{array}$

Conclusion:

The cost of one ream of paper is $7.5 and the cost of one inkjet cartridge is $35.