Answer
Yes. It is possible to score exactly 100 points with all seven darts landing on the board.
Work Step by Step
This problem is a simple system of equations. This can be set up as:
Legend: x=19 and y=8, in terms of the values on the dartboard.
1st: $x+y=7$
2nd: $19x+8y=100$.
Using multiplication to achieve the same coefficients for y, we can multiply the 1st equation by 8.
This will give us an equation of $8x+8y= 56$. We can then subtract the 2nd equation from this new equation.
$8x+8y= 56$ -
$19x+8y=100$
This will result in $-11x= 44$. Dividing both sides by -11 will give a value of $x=4$.
Substituting x=4 into the first equation will allow us to solve for y.
$4+y=7$ which simplifies to $y=3$
This solutions means that 100 can be scored with 4 19's and 3 8's.
