The sum of andre and brandons scores on a math quiz is 180. andre score is 2 times as much as 30 less than brandons score. find each students quiz score

To solve this word problem, we are going to write a system of equations, letting the variable a represent Andre's test score, and the variable b represent Brandon's test score.  

We know that Andre and Brandon's combined test score is 180, or 

a+b = 180

We also know that Andre's score is twice as much as 30 less than Brandon's score, or 

2a = b - 30

Now, we just need to solve the system of equations by substitution, as this is the easiest method for this specific problem.

When simplified, a+b=180 equals a=180-b

Now, if we use this equation of a in substitution for the other equation, we will get our answer.

2(180-b) = b-30

When we use the distributive property to simplify the left side of the equation, we get:

360-2b=b-30

When we further reduce the equation by adding 2b to both sides of the equation, we get:

360 = 3b-30

Next, we have to add 30 to both sides to get the variable alone on the right side of the equation, resulting in the equation:

390=3b

Finally, we divide both sides by 3 to separate the coefficient from the variable b

130=b 

Now, we have to substitute our solution for the variable b into the original equation.

a+b=180
a+130=180
a=50

Therefore, Brandon's test score was 130, and Andre's test score was 50.