a team made 53 successful shots. They were a combination of​ 1- and​ 2-point shots. The team scored 87 points in all. Write and solve a system of equations to find the number of each type of shot.

Answer 1

Let's denote the number of 1-point shots as x and the number of 2-point shots as y.

The total number of successful shots is given in the problem statement as 53, so we can form the equation:

x + y = 53 [Equation 1]

The total number of points scored is also given as 83. Since 1-point shots contribute 1 point each and 2-point shots contribute 2 points each, we can write the following equation:

1x + 2y = 87 [Equation 2]

Now, we have a system of equations with two variables. The simplest method of solving it is to use the substitution method.

From equation 1, we can first solve for x and get the following expression:

x = 53 - y

Now, substitute this expression for the x variable in equation 2:

1(53 - y) + 2y = 87

Simplify and solve for y:

53 - y + 2y = 87

53 + y = 87

y = 34

We now have the variable for y. Substitute it back into the expression for x we found earlier:

x = 53 - y

x = 53 - 34

x = 19

Therefore the number of 1-point shots (x) is 19 and the number of 2-point shots (y) is 34.

Answer 2

So first, I'm going to use the letter A to represent 1-point shots, and the letter B to represent 2-point shots. Then I'm going to rewrite what we already know using math symbols instead of words. So

"a team made 53 successful shots " means the total number of shots is their 1-pointers and 2-pointers added together. or

A + B = 53.

I also know their score was 87 points in all, so

1A + 2B = 87.

I'm multiplying A by 1 because each shot was worth one point and B by 2 because each of those was worth 2 points.

From there, I choose an equation, (I like looking for the simplest looking one) and solve it so that

A = (something). Then I plug that answer into the second equation, which I will solve for

B = (something else)

I choose the first equation to solve for A because it looks easiest. I take A + B = 53, and I undo (+B) by subtracting B from both sides. Now I have

A = 53 - B.

We can substitute (53 - B) anywhere I see the letter A. So now I'm going to rewrite my second equation using (53 - B) anywhere I see the letter A. When I'm done, it looks like this:

1A + 2B = 87 becomes 1(53 - B) + 2B = 87

I combine like terms; -B + 2B = B, so now my equation says

53 + B = 87

My last step is to subtract 53 from both sides, which gives me

B = 87-53 which my calculator tells me is B = 34.

That tells me how many 2-point shots the team made. Now I just have to choose one of my 2 original equations, use 34 anywhere I see the letter B (substitution again) and solve for A.

I choose the first equation because it's easier

A + B = 53; Using 34 instead of B, I get A + 34 = 53.

My last step now is to subtract 34 from both sides, which means that

A = 53 -34. My calculator says A = 19

So the team scored 19 1-pointers and 34 2-pointers. That's 53 shots total, and a score of 87

Answer 3

Let x be 1-point shots and y be 2-point shots.

x+y=53

x+2y=87

x=53-y

53-y+2y=87

y=34

x=19