Question

Mr. Martin’s math test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points. x + y = 29, 5x + 2y = 100 How many problems of each point value are on the test? 10 problems worth 5 points and 25 problems worth 2 points 14 problems worth 5 points and 15 problems worth 2 points 16 problems worth 5 points and 13 problems worth 2 points 15 problems worth 5 points and 13 problems worth 2 points

Answer 1

Answer:

14 problems worth 5 points and 15 problems worth 2 points

14 x 5 = 70

15 x 2=  30

70 + 30= 100

14+15 = 29   5 x 14 + 2 x 15=100

Answer 2

Answer:

Option 2.

Step-by-step explanation:

Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.

Mr. Martin’s math test, which is worth 100 points, has 29 problems.

$x+y=29$               .... (1)

$5x+2y=100$         ..... (2)

Multiply equation (1) by 2.

$2x+2y=58$         .... (3)

Subtract equation (3) from equation (2), to eliminate the variable y.

$5x+2y-(2x+2y)=100-58$

$5x+2y-2x-2y=42$

Combined like terms.

$(5x-2x)+(2y-2y)=42$

$3x=42$

Divide both sides by 3.

$x=14$

The value of x is 14.

Substitute x=14 in equation (1).

$14+y=29$

Subtract 14 from both sides.

$y=29-14$

$y=15$

The value of y is 15.

It means 14 problems worth 5 points and 15 problems worth 2 points.

Therefore, the correct option is 2.