Chapter 6.4, Problem 13PPE

a.

To determine

To calculate: system of equations that models this situation.

Answer to Problem 13PPE

  $-2.5$ pennies and $17.5$ quarters.

Explanation of Solution

Calculation:

Let’s say you have $x$ pennies and $y$ quarters.

Now, the total coins should be 15, $\therefore x+y=15$ …(i)

Now, the worth of $x$ pennies are, $\$0.01x$ and the worth of $y$ quarters are, $\$0.25y$

Now, the total worth is, $\$4.35$

  $\therefore 0.01x+0.25y=4.35$

  $\therefore x+25y=435$ …(ii)

Now, let’s substitute $x$ from the equation (i) to equation (ii),

  $x+25(15-x)=435$

  $x+375-25x=435$

  $\therefore x=-2.5$

By putting the value of $x$ in equation (i), we get, $y=15+2.5=17.5$

b.

To determine

To calculate: Explain reasonability of the problem.

Answer to Problem 13PPE

Not reasonable

Explanation of Solution

Calculation:

Solution we got is, $-2.5$ pennies and $17.5$ quarters.

Now, number of coins can’t be negative. Also, it should be positive integers only. Here, we are getting negative and non-integer values for number of coins. Therefore, the solution is not reasonable in terms of original problem.