algebra question

Question

In a basketball game, a regular basket was worth 2 points and a long-distance basket was worth 3 points. If there were 45 baskets in a game and 96 points total, how many regular baskets r and long-distance baskets l were made?

Answer 1

Hi Gin,

Let's define our variables first.

x = number of regular baskets

y = number of 3-pointers

Since we know 45 baskets were made, we can write the equation.

x+y = 45

We know each x basket is worth 2 points and each y basket is worth 3 points. Since we know there were 95 points in total, we can write a second equation.

2x + 3y = 95

Now we can solve our system of equations.

First, let's solve for x in the first equation.

x+y =45

x = 45 - y

Next, lets plug in this x value to our second equation.

2(45 - y) + 3y = 95

(Distribute)

90 - 2y + 3y = 95

(Combine like terms)

90 + y = 95

(Subtract 90 from both sides)

y = 5

Now, lets plug this y value into our first equation

x + 5 = 45

x = 40

That means there were 5 long distances baskets and 40 regular baskets made.

Hope this helps!

Emily

Answer 2

This is a system of linear equations question as there are two conditions in the problem, points scored and baskets made along with two variables, 2 pt (r) and 3 pt shots (l)

So r represents the number of 2 pt shots made and l represents the number of 3 pt shots made

First condition: points total of 96 points made up of 2 pt and 3 pt 2r + 3l = 96

Second condition: baskets made 45 r + l = 45

Once you have your system set up, you can solve by 3 methods, 1) substitution, 2) elimination, or 3) graphing

I will choose elimination

If I multiply the second equation by -2 I get -2r -2l = -90

Add that to the first equation and the r variable is eliminated leaving l = 6, so 6 3 pt baskets

Substitute that answer back into either equation, I will choose the second,

r + 6 = 45 so r = 39 or 39 2 pt baskets

Check: 2(39) + 3(6) = 78 + 18 = 96

39 + 6 = 45