Chapter 4.2, Problem 40E

(a)

To determine

To find: the most money received by the sibling and the least money.

Answer to Problem 40E

The most money received by sibling B and the least money received by sibling A.

Explanation of Solution

Given:

Consider the graph describes siblings A spending

  

Consider the table describes the sibling B's spending

Week x	Money Left, y
1	$100
2	$75
3	$50
4	$25

Draw the graph for the set of data

  

Consider the equation $y=-22.5x+90$ for the sibling C's spending.

Draw the graph for the equation

  

Calculation:

From the above three graphs for the siblings, compare the y-intercepts which indicates the money received.

Conclusion:

Therefore, the most money received by sibling B and the least money received by sibling A.

(b)

To determine

To find: the fastest rate spends money by the sibling and the slowest rate.

Answer to Problem 40E

The sibling who spend money at fastest rate is sibling A and the sibling who spend money at slowest rate is sibling B.

Explanation of Solution

Calculation:

Find the rates for each sibling Rate of spend money for sibling A is

  $\begin{array}{l}{r}_A=\frac{20-50}{4-2}\\ =\frac{-30}{2}\\ =-15\end{array}$

Rate of spend money for sibling B is

  $\begin{array}{l}{r}_B=\frac{75-100}{2-1}\\ =\frac{-25}{1}\\ =-25\end{array}$

Rate of spend money for sibling C is

  $r_C=-22.5$

Conclusion:

Therefore, the sibling who spend money at fastest rate is sibling A and the sibling who spend money at slowest rate is sibling B.

(c)

To determine

To find: the sibling runs out of money first and last.

Answer to Problem 40E

The sibling runs out of money first is sibling A and the sibling runs out of money last is sibling B.

Explanation of Solution

Calculation:

Compare the x-intercept of line for each sibling graph which shows the week at which the money will run out.

Conclusion:

Therefore, the sibling runs out of money first is sibling A and the sibling runs out of money last is sibling B.