A math test has 25 problems. Some are worth 2 points and some are worth 3 points. The test is worth 60 points. How many problems are worth 2 points and how many problems are worth 3 points?

There are 15 problems worth 2 points and there are 10 problems worth 3 points

Step-by-step explanation:

To realize this problem we will perform two equations

one will represent the number of problems and another the number of points

x would be the number of problems worth 2 points and y the amount worth 3 points

x + y = 25

(x * 2) + (y * 3) = 60

we clear the x of the first equation

x + y = 25

x = 25 - y

and replace the x with (25 - y) in the second equation

(x * 2) + (y * 3) = 60

( (25 - y) * 2) + (y * 3) = 60

50 - 2y + 3y = 60

-2y + 3y = 60 - 50

y = 10

Now we return to the first equation and replace y with 10

x = 25 - y

x = 25 - 10

x = 15

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