Question

Three-fourths through the soccer season Gustafo has 24 goals. He averages 4 goals per game. How many more games will it take Gustafo to have at least 40 goals before the season is over?

Answer 1

Gustafo will never reach 40 goals before the season is over, unless he makes more goals per game.

Explanation:

Here are our quantities:
1) He has 24 goals now
2) His average is 4 goals per game
3) He has played `3/4`ths of the season

With 24 goals total and and average of 4 goals per game, we can calculate how many games have been played so far by dividing 24 by 4:
`24/4=6" "lArr` so 6 games played so far

Those 6 games represent `3/4`ths of the season, witch has a total of `x` games:
`6=3/4*x" "` Multiply each side by 4
`6*4=3/cancel4*x*cancel4" "`

`24=3*x" "` Divide each side by 3

`24/3=cancel3/cancel3*x`
`x=8" "`

So there are 8 games total in the season. Since 6 games have been played, there are only 2 left. With 4 goals per game Gustafo could make 8 more goals. Adding 8 goals to the 24 he already has gives a total of 32 goals. In order to achieve his 40 goal objective, he would have to score more goals in each of the remaining games.

Answer 2

The count of additional games to achieve at least a total of 40 goals
4 games.

Explanation:

`color(magenta)("Even though the football season is "3/4" the way through, there")` `color(magenta)("is no limit specified in the question on the number of games that may be played")` `color(magenta)("in the last quarter of the season.")`

`color(blue)("Goals needed to reach 40")`

`40-24= 16`

Using ratio for the average rate of goals and games we have

`("games")/("goals") ->1/4`

But we need to change the 4 goals into 16 goals.

`color(green)(("games")/("goals") ->1/4)color(red)( = 1/4xx1)=1/4xx4/4=color(purple)(4/16)`