A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?

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Mathematics

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A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?

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smayra1191 smayra1191 · Answer 1 · 2025-03-28T00:02:27-04:00

Answer:

5 points question is 8

and 2 points questions is 30 !!

Step-by-step explanation:

Let the number of 5 points questions be x and number of the 2 points questions be y !!

Given :- The paper has 38 problems

i.e,

number of 5 points Q + number of 2point Q = 38

=> x + y = 38

=> x = 38 - y .... ( i )

And , The test worth 100 pts :-

There must be x number of Questions which carry 5 points and there must y number of questions which carries 2 points ( as assume above )

so, 5x + 2y = 100 .... ( ii )

Putting value of the x in ( ii )

5 ( 38 - y ) + 2y = 100

190 - 5y + 2y = 100

- 3y = - 90

y = 30

Putting value of y in ( i )

x = 38 - y

x = 38 - 30

x = 8

So, the Number of 5points Question is

x = 8

and , the number of 2 points questions is y = 30 !!