Sophia’s math test is worth 130 points and has 40 problems. each problem is worth either 4 points or 3 points. how many of each question type were on the test? the test had 30 4-point questions and 10 3-point questions. the test had 10 4-point questions and 30 3-point questions. the test had 28 4-point questions and 12 3-point questions. the test had 25 4-point questions and 10 3-point questions.

To solve this problem, we must set up a system of equations.  We are going to let the first type of problem (worth 4 points) be represented by the variable a, and the second type of problem (worth 3 points) be represented by the variable b.

We know that there were 40 problems and the test was worth 130 points, therefore we can construct the following equations.

a+b =40
4a + 3b = 130

To solve this system of equations, we are going to use substitution.  To do this, we are going to subtract the variable a from both sides of the first equation to get the variable b alone.  This gives us the equation: b = 40-a

We are going to substitute this expression for b into the other equation, giving us:
4a + 3(40-a) = 130

We must simplify this equation using the distributive property and by combining like terms, as seen below:
4a + 120 - 3a = 130
a + 120 = 130
a = 10
Therefore, there are 10 four-point questions on the test.  We know that the total number of questions must be 40, therefore there are 30 three- point questions on the test.  

Your answer is option 2: The test had 10 4-point questions and 30 3-point questions.

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