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?

2 Answers
Oct 10, 2016

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.

Oct 10, 2016

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) #