Question

Write an inequality for the word problem and answer the question about the inequality. The faculty team scored less than half as many points as the varsity team. A total of 100 points was scorered. If x represents the number of points that the varsity team scored Could x = 60

Answer 1

From the exercise we can indentify the following

• x, = number of points that the varsity team scored

,

• y ,= number of points that the faculty team scored

`\begin{gathered} x+y=100\to(1) \\ y<(1)/(2)x\to(2) \end{gathered}`

Let's clear y in (1) to be able to replace in (2)

`\begin{gathered} y=100-x\to(1) \\ 100-x<(1)/(2)x\to(1)\text{ in (2)} \\ (1)/(2)x+x>100 \\ (3)/(2)x>100 \\ x>(100\cdot2)/(3) \\ x>(200)/(3) \\ x>66.6666 \\ x>67 \end{gathered}`

The answer is x cannot be equal to 60 because they have to be at least 67 points to comply with the inequality