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

Question

22-02-2019
Mathematics

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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

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Аноним Аноним · Answer 1 · 2019-02-22T01:24:33+01:00

Аноним Аноним

22-02-2019

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

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erinna erinna · Answer 2 · 2019-10-01T08:53:51+02:00

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.

[tex]x+y=29[/tex] .... (1)

[tex]5x+2y=100[/tex] ..... (2)

Multiply equation (1) by 2.

[tex]2x+2y=58[/tex] .... (3)

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

[tex]5x+2y-(2x+2y)=100-58[/tex]

[tex]5x+2y-2x-2y=42[/tex]

Combined like terms.

[tex](5x-2x)+(2y-2y)=42[/tex]

[tex]3x=42[/tex]

Divide both sides by 3.

[tex]x=14[/tex]

The value of x is 14.

Substitute x=14 in equation (1).

[tex]14+y=29[/tex]

Subtract 14 from both sides.

[tex]y=29-14[/tex]

[tex]y=15[/tex]

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.