SOLUTION: In a basketball, a field goal is either 2 or 3 points. In a college basketball tournament, Jim made 73 more 2-point field goals that 3-point field goals. If he scored a total of 21

Question 1185268: In a basketball, a field goal is either 2 or 3 points. In a college basketball tournament, Jim made 73 more 2-point field goals that 3-point field goals. If he scored a total of 216 goals in the tournament how many 3-point field goals did he make?
2x+3y=216
2x+73=3y
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
In a basketball, a field goal is either 2 or 3 points. In a college basketball tournament,
Jim made 73 more 2-point field goals that 3-point field goals. If he scored a total of 216 goals in the tournament
how many 3-point field goals did he make?
2x+3y=216
2x+73=3y
~~~~~~~~~~~~~~~~~~~

            According to the terminology, used in the problem, you should DISTINCT the goals and the points.

            To distinct them is IMPORTANT to write equation correctly.

The system of equation in your post is INCORRECT (is inadequate to the problem). The correct system is THIS 2x + 3y = 216 (1) x = y + 73 (2) To solve the system, substitute expression (2) for x into equation (1). You will get then a single equation fot y, which is the unknown variable under the problem's question 2*(y + 73) + 3y = 216 Simplify and find y 2y + 146 + 3y = 216 2y + 3y = 216 - 146 5y = 70 y = 70/5 = 14. ANSWER. 14 3-score goals.

Solved.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

I will assume you have posted the problem incorrectly; the information as given is self-contradictory.

The given information is that the number of 2-point field goals was 73 more than the number of 3-point field goals. That means either the number of 3-point field goals was an even number and the number of 2-point field goals was odd, or vice versa. In either case, one of the numbers was even and the other was odd, so the sum of the two numbers is odd.

But the problem says he scored 216 goals, which is an even number....

In order to help you with this, I will assume that the given information was supposed to be that he scored 216 POINTS in the tournament.

Thank you for showing the work you did to start on the problem. Not even 1 out of every 100 students who post problems to this forum follow the instructions for posting and do that.

In this case, the work you show lets me know how I can help you....

Especially when first learning to solve problems using algebra, it is important to take the time to write down the definitions of the variables you are going to use; doing that makes it MUCH easier to write equations that make sense and mean what you want them to say.

The variables involved in this problem are the numbers of 2-point and 3-point field goals Jim scored in the tournament. So let's start by writing out definitions of our variables.

Let x = number of 2-point field goals
Let y = number of 3-point field goals

Your first equation then makes perfect sense. 2x is the total number of points from x 2-point field goals; 3y is the total number of points from y 3-point field goals, and 216 is the total number of points.

2x+3y=216 (points from 2-point field goals, plus points from 3-point field goals, equals total points)

But now with the definitions of x and y written down, your second equation makes no sense.

The expressions 2x and 3y in your second equation are the numbers of points from 2-point and 3-point field goals; the "73" has nothing to do with those numbers. So your second equation

2x+73=3y

makes no sense.

Instead, 73 is the difference between the number of 2-point field goals (x) and the number of 3-point field goals (y):

x-y=73

Now you have two equations in x and y that you can use to solve the problem:

2x+3y=216
x-y=73

I'll let you have the satisfaction of solving that pair of equations to find the answer to the problem.

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