Chapter 5.1, Problem 57PFA

To determine

Match the option which represent the situation.

Answer to Problem 57PFA

Option C is correct.

Explanation of Solution

Given:

At the school store, Raul bought 4 note books and 2 pens. Helen bought 5 notebooks. If Helen spent at least as much as Raul, which statement about the cost of notebooks and pens is true?

Options are:

A: If pens cost $1.50, then notebooks must cost at least $5

B: If pens cost $1.50, then notebooks must cost more than $5

C: If pens cost $2.50, then notebooks must cost at least $5

D: If pens cost $2.50, then notebooks must cost no more than $5.

Concept Used:

Let the cost of notebook is $N and the cost of 1 pen = $P

Raul bought 4 note books and 2 pens. Total cost: $(4N+2P)

Helen bought 5 notebooks. Total cost $ 5N.

Condition given: Helen spent at least as much as Raul

This means Raul`s spend $\ge$ Helen`s spend

Inequality: $\text{4N+2P}\ge \text{5N}$

Calculation:

Inequality: $\text{4N+2P}\ge \text{5N}$

Solve:

  $\begin{array}{l}\text{4N+2P}\ge \text{5N}\\ \text{4N}-\text{4N+2P}\ge \text{5N}-\text{4N}\\ \text{2P}\ge \text{N}\end{array}$

This means cost of 2 pens at least cost of 1 notebook.

C: If pens cost $2.50, then notebooks must cost at least $5

Option C is correct.

Thus, option C is correct.