91Ó°ÊÓ

An inequality is an algebraic expression with one or more variables, containing one of the symbols; $<,>,≤,â‰\yen$

A receiving yard is worth 5 points, a touchdown is worth 100 points and a game with 1000 points or more is considered to be a good game.

The statistics of 3 games is given as:

Let $x$be the number of receiving yards that Moss gets in a game and $y$be the number of touchdowns that Moss scores in a game.

Since each receiving yard is worth 5 points and each touchdown is worth 100 points, the total points earned in a game is evaluated as $5x+100y$.

It is given that a game in which 1000 points or more are earned is a good game. Then, by the problem, a game is a good game if $5x+100yâ‰\yen 1000$.

This is the required inequality.

It is obvious that the number of touchdowns cannot be negative. So, $yâ‰\yen 0$. However, receiving yardage may be negative or positive. So, there is no restriction on $x$.

Graph the obtained inequality $5x+100yâ‰\yen 1000$with the restriction $yâ‰\yen 0$as follows:

It is clear, from the table that for Game 1, $x=168$and $y=3$.

Put $x=168$and $y=3$in the obtained inequality $5x+100yâ‰\yen 1000$to get,

$\begin{array}{l}5\left(168\right)+100\left(3\right)â‰\yen 1000\\ 840+300â‰\yen 1000\\ 1140â‰\yen 1000\end{array}$

This implies that the given inequality is true for $x=168$and $y=3$. Thus, Game 1 is a good game.

Similarly, from the table, for Game 2, $x=144$and $y=2$.

Put $x=144$and $y=2$in the obtained inequality $5x+100yâ‰\yen 1000$to get,

$\begin{array}{l}5\left(144\right)+100\left(2\right)â‰\yen 1000\\ 720+200â‰\yen 1000\\ 920â‰\yen 1000\end{array}$

This is a contradiction and thus implies that the given inequality is false for $x=144$and $y=2$. So, Game 2 is not a good game.

Finally, from the table, for Game 3, $x=136$and $y=1$.

Put $x=136$and $y=1$in the obtained inequality $5x+100yâ‰\yen 1000$to get,

$\begin{array}{l}5\left(136\right)+100\left(1\right)â‰\yen 1000\\ 680+100â‰\yen 1000\\ 780â‰\yen 1000\end{array}$

This is a contradiction and thus implies that the given inequality is false for $x=136$and $y=1$. So, Game 3 is also not a good game.

Thus, only Game 1 is a good game.