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16 June, 23:41

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

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  1. 17 June, 02:19
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    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.
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