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Question

Maria and James received their scores on three exams. On the first exam, Maria’s score was 12 points less than James’s score. On the second exam, Maria’s score was 5 points greater than James’s score. If James’s average (arithmetic mean) score on the three exams was 4 points lower than Maria’s average score on the three exams, then James’s score on the third exam was how many points lower than Maria’s score?

Answer Choices

A. $7$
B. $17$
C. $19$
D. $23$
E. $29$

Steps

Explanation	Calculations	Help
$We create variables for Maria's and James's scores on each of the three exams.$	$M_{1} = Maria’s first exam score M_{2} = Maria’s second exam score M_{3} = Maria’s third exam score J_{1} = James’s first exam score J_{2} = James’s second exam score J_{3} = James’s third exam score$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "On the first exam, Maria's score was 12 points less than James's score." into an equation.$	$M_{1} = J_{1} - 12$	Theory & Tactics Method Card TRANS1-D Click to view full details
$We translate "On the second exam, Maria's score was 5 points greater than James's score." into an equation.$	$M_{2} = J_{2} + 5$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "James's average (arithmetic mean) score on the three exams was 4 points lower than Maria's average score on the three exams." into an equation.$	$\frac{J _{1} + J _{2} + J _{3}}{3} = \frac{M _{1} + M _{2} + M _{3}}{3} - 4$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We eliminate the denominators by multiplying both sides of the equation by 3.$	$J_{1} + J_{2} + J_{3} = M_{1} + M_{2} + M_{3} - 12$
$We substitute the expressions for M_{1} and M_{2} from earlier steps into the equation.$	$J_{1} + J_{2} + J_{3} = (J_{1} - 12) + (J_{2} + 5) + M_{3} - 12$
$We simplify and cancel common terms to isolate J_{3} .$	$J_{1} + J_{2} + J_{3} = J_{1} + J_{2} + M_{3} - 12 + 5 - 12 J_{1} + J_{2} + J_{3} = J_{1} + J_{2} + M_{3} - 19 J_{3} = M_{3} - 19$

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Final Answer

C

Question

Maria and James received their scores on three exams. On the first exam, Maria’s score was 12 points less than James’s score. On the second exam, Maria’s score was 5 points greater than James’s score. If James’s average (arithmetic mean) score on the three exams was 4 points lower than Maria’s average score on the three exams, then James’s score on the third exam was how many points lower than Maria’s score?

Answer Choices

A. $7$
B. $17$
C. $19$
D. $23$
E. $29$

Steps

Explanation	Calculations	Help
$We create variables for Maria's and James's scores on each of the three exams.$	$M_{1} = Maria’s first exam score M_{2} = Maria’s second exam score M_{3} = Maria’s third exam score J_{1} = James’s first exam score J_{2} = James’s second exam score J_{3} = James’s third exam score$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "On the first exam, Maria's score was 12 points less than James's score." into an equation.$	$M_{1} = J_{1} - 12$	Theory & Tactics Method Card TRANS1-D Click to view full details
$We translate "On the second exam, Maria's score was 5 points greater than James's score." into an equation.$	$M_{2} = J_{2} + 5$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "James's average (arithmetic mean) score on the three exams was 4 points lower than Maria's average score on the three exams." into an equation.$	$\frac{J _{1} + J _{2} + J _{3}}{3} = \frac{M _{1} + M _{2} + M _{3}}{3} - 4$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We eliminate the denominators by multiplying both sides of the equation by 3.$	$J_{1} + J_{2} + J_{3} = M_{1} + M_{2} + M_{3} - 12$
$We substitute the expressions for M_{1} and M_{2} from earlier steps into the equation.$	$J_{1} + J_{2} + J_{3} = (J_{1} - 12) + (J_{2} + 5) + M_{3} - 12$
$We simplify and cancel common terms to isolate J_{3} .$	$J_{1} + J_{2} + J_{3} = J_{1} + J_{2} + M_{3} - 12 + 5 - 12 J_{1} + J_{2} + J_{3} = J_{1} + J_{2} + M_{3} - 19 J_{3} = M_{3} - 19$

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Final Answer

C