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Question

Beth and Dylan recorded the number of units they produced in three consecutive months. In the first month, Beth produced 8 more units than Dylan. In the second month, Beth produced 6 more units than Dylan. If Dylan’s average production over the three months was 5 units greater than Beth’s average, then Dylan’s production in the third month was how many units greater than Beth’s production?

Answer Choices

A. $23$
B. $29$
C. $21$
D. $31$
E. $43$

Steps

Explanation	Calculations	Help
$We create variables for Beth's and Dylan's production in each of the three months.$	$B_{1} = Beth’s first month production B_{2} = Beth’s second month production B_{3} = Beth’s third month production D_{1} = Dylan’s first month production D_{2} = Dylan’s second month production D_{3} = Dylan’s third month production$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "In the first month, Beth produced 8 more units than Dylan." into an equation.$	$B_{1} = D_{1} + 8$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "In the second month, Beth produced 6 more units than Dylan." into an equation.$	$B_{2} = D_{2} + 6$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "Dylan's average production over the three months was 5 units greater than Beth's average" into an equation.$	$\frac{D _{1} + D _{2} + D _{3}}{3} = \frac{B _{1} + B _{2} + B _{3}}{3} + 5$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS3-F Click to view full details
$We eliminate the denominators by multiplying both sides by 3.$	$D_{1} + D_{2} + D_{3} = B_{1} + B_{2} + B_{3} + 15$
$We substitute the expressions for B_{1} and B_{2} into the equation.$	$D_{1} + D_{2} + D_{3} = (D_{1} + 8) + (D_{2} + 6) + B_{3} + 15$
$We simplify and cancel common terms to isolate D_{3} .$	$D_{1} + D_{2} + D_{3} = D_{1} + D_{2} + B_{3} + 8 + 6 + 15 D_{1} + D_{2} + D_{3} = D_{1} + D_{2} + B_{3} + 29 D_{3} = B_{3} + 29$	Theory & Tactics Method Card CALC1-A Click to view full details

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Final Answer

B

Question

Beth and Dylan recorded the number of units they produced in three consecutive months. In the first month, Beth produced 8 more units than Dylan. In the second month, Beth produced 6 more units than Dylan. If Dylan’s average production over the three months was 5 units greater than Beth’s average, then Dylan’s production in the third month was how many units greater than Beth’s production?

Answer Choices

A. $23$
B. $29$
C. $21$
D. $31$
E. $43$

Steps

Explanation	Calculations	Help
$We create variables for Beth's and Dylan's production in each of the three months.$	$B_{1} = Beth’s first month production B_{2} = Beth’s second month production B_{3} = Beth’s third month production D_{1} = Dylan’s first month production D_{2} = Dylan’s second month production D_{3} = Dylan’s third month production$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "In the first month, Beth produced 8 more units than Dylan." into an equation.$	$B_{1} = D_{1} + 8$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "In the second month, Beth produced 6 more units than Dylan." into an equation.$	$B_{2} = D_{2} + 6$	Theory & Tactics Method Card TRANS1-C Click to view full details
$We translate "Dylan's average production over the three months was 5 units greater than Beth's average" into an equation.$	$\frac{D _{1} + D _{2} + D _{3}}{3} = \frac{B _{1} + B _{2} + B _{3}}{3} + 5$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS3-F Click to view full details
$We eliminate the denominators by multiplying both sides by 3.$	$D_{1} + D_{2} + D_{3} = B_{1} + B_{2} + B_{3} + 15$
$We substitute the expressions for B_{1} and B_{2} into the equation.$	$D_{1} + D_{2} + D_{3} = (D_{1} + 8) + (D_{2} + 6) + B_{3} + 15$
$We simplify and cancel common terms to isolate D_{3} .$	$D_{1} + D_{2} + D_{3} = D_{1} + D_{2} + B_{3} + 8 + 6 + 15 D_{1} + D_{2} + D_{3} = D_{1} + D_{2} + B_{3} + 29 D_{3} = B_{3} + 29$	Theory & Tactics Method Card CALC1-A Click to view full details

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Final Answer

B