Question

In a recent season,Monique Currie of the Duke Bule Devils scored 635 point.She made a total of 365 shots, include 3 point field goals, 2-point field goal,and 1 point free throws.She made 76 more 2 -point field goals than free throw and 77 more free throw than 3-point field goals.Find the number of each type of shot she made.

Answer 1

Are you sure it's 635? and not 653?

Answer 2

Okay, lets suppose Monique made x 3-point shots, y 2-point shots, and z 1-point shots. Then we have:
x + y + z = 365
y = z + 76
z = x + 77

Then y = x + 76 + 77 = x + 153.
Then x + y + z = x + x + 153 + x + 77 = 3x + 230 = 365. Thus, x = 45.
Then z = 45 + 77 = 122.
Then y = 122 + 76 = 198.

We can check this easily - 198 + 122 + 45 = 365 and 3(45) + 2(198) + 1(122) = 135 + 396 + 122 = 653

(I assume, since the system was solved without using the equation 3x + 2y + z = 635, that it should be 3x + 2y + z = 653)

Answer 3

I thought so. I had this loaded up before I asked the question:

Ok. Let's set this up easy. Make x =1point free throws. Let's set the relation between 1,2, and 3. She made 76 more 2's and 77 more 1's than 3's. so we have x +76 = 2's and x -77 = 3's. So with a total of 365 shots:
365 = (x) + (x+76) + ( x - 77)
365 = x + x + x -1
366 = 3x
122 = x = # of free throws. Thus (x+76) = 122 + 76 = 198 = # of 2's and x - 77 = 122 -77 = 45 = # of 3's.

Check your work
(122 * 1) + ( 198*2) + (45*3) = 635
122+396+135=635
653 =/= 635.....

Answer 4

sorry I made mistake
In a recent season,Monique Currie of the Duke Bule Devils scored 635 point.She made a total of 356 shots, include 3 point field goals, 2-point field goal,and 1 point free throws.She made 76 more 2 -point field goals than free throw and 77 more free throw than 3-point field goals.Find the number of each type of shot she made.

Answer 5

Let x - 77 - 3 point field goal
x + 76 - 2 point field goal
x - 1 point free throw

equations: x + x + 76 + x-77 = 356

3x -1 = 356
3x = 356 + 1
3x = 357
x = 119

she made 119 free throws, 196 2-point field goals, and 42 3-point field goal.

checking: 119 + 195 + 42 = 356

314 + 42 = 356

356 = 356

Answer 6

she made 119 free throws, 195 2-point field goals, and 42 3-point field goal. I mean.

Answer 7

Satisfied?

Answer 8

ty,yes