Amath test has a total of 20 problems some problems are worth two points and some are worth three points the whole test is worth 452 points how many three-point problems were there

There were 12 questions worth 3 points

Step-by-step explanation:

Let x = 2 point questions

let y = 3 point questions

What we know:

x + y = 20 (questions)

so to solve for x we tweak our equation:

x = 20 - y

Now we need an equation to explain out question set up:

2x (2 point questions)

3y (2 point questions)

2x + 3y = 52 (52 being our total possible points)

Now we take our x = 20 - y and substitute it into our 2x + 3y = 52 equation.

2(20 - y) + 3y = 52

Next we distribute the 2 through the parenthesis:

40 - 2y + 3y = 52

Now, gather the like terms:

40 + y = 52

Subtract 40 from both sides:

y = 12

Revisit x + y = 20 and sub 12 in for Y:

x + 12 = 20

x = 8

8 2-point questions would be 16 points

12 3-point questions would be 36 points

16 + 36 = 52 (which matches the max value of our test)