Question

In a basketball game, Marlene made 16 fields goals. Each of the field goals were worth either 2 points or 3 points, and Marlene scored a total of 39 points from field goals. Find the number of two point field goals made.

Answer 1

Answer: She made 9 two-point field goals

Step-by-step explanation: First of all let the 2-point goals be represented by letter a and the 3-point goals be represented by letter b. If she made 16 field goals in total that means she recorded a + b = 16.

Also she scored a total of 39 points from field goals which means she also recorded, 2a + 3b = 39. So we now have a pair of simultaneous equations which are as follows;

a + b = 16 ———(1)

2a + 3b = ———(2)

From equation (1), make a the subject of the equation, hence a = 16 - b

Substitute for the value of a into equation (2)

2(16 - b) + 3b = 39

32 - 2b + 3b = 39

3b - 2b = 39 - 32

b = 7

Substitute for the value of b into equation (1)

a + b = 16

a + 7 = 16

Subtract 7 from both sides of the equation

a = 9

Since two-point field goals have been represented by a, then she scored 9 two-point goals.

Answer 2

9 two-point field goals

Explanation:

In this case we can solve it using a 2x2 system of equations, like this:

let x: 2 point fields goals

let y: 3 point fields goals

So:

2 * x + 3 * y = 39

x + y = 16 => x = 16 - y

Replacing, we are left with that:

2 * (16 - y) + 3 * y = 39

32 - 2 * y + 3 * y = 39

- 2 * y + 3 * y = 39 - 32

y = 7

Now to calculate x:

x = 16 - 7

x = 9

Which means I score 9 two-point field goals and 7 3-point field goals