Question 800618: This basketball season, Collin scored 7 less points than Antonio, Shaun scored twice as many points as Antonio, and Julio scored 5 less than 3 times as many points as Antonio. If all 4 players scored a total of 303 points this season, how many points did each player score?
Number of points scored by Antonio:
Number of points scored by Collin:
Number of points scored by Shaun:
Number of points scored by Julio:
Answer by VictoryStar(6)   (Show Source):
You can put this solution on YOUR website! If 303 points were scored in total, on one side of the equation, would be =303 (Recommended to be the right side)
Use Collin's points as "X", a number you do not currently know.
So far, (Not complete yet), we have x=303
Collin, however, did 7 less points than Antonio. But since Collin is X, it can be re-written as Antonio scored 7 more points than Collin, which gives us X+7. Combine these results and so far you obtain
X+X+7=303
Shaun scored two times more than the amount Antonio scored, and since we defined Antonio's points as X+7, that multiplied by two (X times 2= 2x, and 7x2 = 14) is 2x+14, we add that to our equation.
So far, we now have X+X+7+2x+14=303
And finally, Julio's points. Julio managed to scored 5 less than 3 times the points of Antonio. Antonio, once more, scored X+7 points. 3 times that becomes 3x+21 (X times 3 is 3x, 7x3 is 21). But however, because he has 5 less, you must subtract that number. 21-5 is 16. Combine this to the equation.
You end up with X+X+7+2X+14+3X+16=303. Combine like terms (All phrases ending with X, are added, similar with the integers.)
Combining like terms gives you with the equation 7x+37=303
Minus 37 from each side to isolate the variable (Keep all of the "X"s on one side.)
Doing so gives you 7x = 266
Divide each side, so you are left with only an X.
This gives you with x = 38.
Simply plug in Collin's number (38), into the other equations, giving you your answer.
Antonio: X+7
Collin: X
Shaun: 2X+14
Julio: 3X+16
Number of points scored by Antonio: 45 (x+7 = 38+7 = 45)
Number of points scored by Collin: 38 (x = 38)
Number of points scored by Shaun: 90 (2x+14 = (2x38)+14 = 76+14 = 90)
Number of points scored by Julio: 130 (3x+16 = (3x38)+16 = 114+16 = 130)
To check your work, simply add the values together, and see if they equal 303.
45 + 38 + 90 + 130
83 + 220
303
Therefore, our answers are correct.
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