Chapter 6.3, Problem 44PPE

To determine

To calculate: Is it possible to score exactly 100 with seven darts that all land on the board.

Answer to Problem 44PPE

It is possible to score exactly 100, with 4 darts hitting 19 points and 3 darts hitting 8 points.

Explanation of Solution

Given information: dart board with score 19 in center and 8 around.

Calculation:

Let’s assume $x$ darts are landing on 19 points and $y$ darts are landing on 8 points

Now, total number of darts are 7, $\therefore x+y=7$.....(i) Now, $x$ darts are scoring $19x$ points and $y$ darts are scoring $8y$ points, and total 100 points are required.

  $\therefore 19x+8y=100$.....(ii)

Substitute $y$ from equation (i) to equation (ii)

  $\therefore 19x+8(7-x)=100$

  $\therefore x=4$

Let’s put the value of $x$ in first equation,

  $\therefore y=3$

Therefore, it is possible to score exactly 100, with 4 darts hitting 19 points and 3 darts hitting 8 points.