Chapter 6.3, Problem 33PPS

a.

To determine

To choose a combination of 9 objects and find the score

Answer to Problem 33PPS

11 points

Explanation of Solution

Given:

Each paper clip is worth 1 point

Each penny is worth 3 points

Calculation:

Let p represent the number of pennies and c represent the number of paper clips.

Let us choose 2 pennies and 5 paperclips

Then to calculate the score,

  $\Rightarrow 2p+5c=2(3)+5(1)=6+5=11$

Conclusion:

Therefore, the score of our choice of combination is 11 points.

b.

To determine

To write and solve the system of equations to find the number of pennies and paper clips

Answer to Problem 33PPS

  $p=3$ and $c=6$

Explanation of Solution

Given:

Number of pennies and paper clips is 15 points

Total of 9 objects are used.

Calculation:

Let p represent the number of pennies and c represent the number of paper clips.

Total number of coins used is 9.

  $\Rightarrow p+c=\mathrm{9....................................}(1)$

The value of coins and paper clips is 15.

  $\Rightarrow 3p+c=\mathrm{15...............................}(2)$

Subtract equation (1) from equation (2).

  $\begin{array}{l}\Rightarrow (3p+c)-(p+c)=15-9\\ \Rightarrow 3p-p+c-c=6\\ \Rightarrow 2p=6\\ \Rightarrow p=3\end{array}$

Substitute the value of p in equation (1).

  $\begin{array}{l}\Rightarrow 3+c=9\\ \Rightarrow c=9-3\\ \Rightarrow c=6\end{array}$

Conclusion:

Therefore, the number of pennies is 3 and the number of paper clips is 6.

c.

To determine

To construct a table showing the number of paper clips and total points when the number of pennies is as given.

Explanation of Solution

Given:

The number of pennies is 0, 1, 2, 3, 4 or 5.

Calculation:

Construct the table as follows.

Pennies (p)	0	1	2	3	4	5
Paper clips (9 - p)	9	8	7	6	5	4
Points	9	11	13	15	17	19

Conclusion:

The above table shows the total points for the mentioned pennies.

d.

To determine

To check if the table matches the result in subpart (b)

Answer to Problem 33PPS

Yes

Explanation of Solution

Since the pennies are 3 points each, 3 of them make 9 points.

Add the 6 points from 6 paper clips and 15 points is obtained.

Using 9 objects, there is no other way of obtaining a score of 15 points.