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Emily and Jack are preparing supplies for a workshop. Emily thinks that the number of notebooks should be twice the number of pens, so N = 2 P, while Jack thinks that the number of pens should be 5 more than one-third of the number of notebooks, so P = \frac{1}{3} N + 5 . How many notebooks should they prepare so that Emily and Jack can agree on the number of pens to prepare?

Explanation	Calculations	Help
$We first create variables to represent the number of notebooks and pens.$	$N = number of notebooks P = number of pens$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate Emily's statement "the number of notebooks should be twice the number of pens" into an equation.$	$N = 2 P$	Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate Jack's statement "the number of pens should be 5 more than one-third of the number of notebooks" into an equation.$	$P = \frac{1}{3} N + 5$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS2-B Click to view full details
$We substitute the expression for N from Emily's equation into Jack's equation to write it in terms of P .$	$P = \frac{1}{3} (2 P) + 5$
$We simplify the right side by multiplying the fraction.$	$P = \frac{2}{3} P + 5$
$We subtract \frac{2}{3} P from both sides to group like terms.$	$P - \frac{2}{3} P = 5$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We simplify the left side and then divide both sides by \frac{1}{3} to solve for P .$	$\frac{1}{3} P = 5 P = 5 \times 3 = 15$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We substitute P = 15 into the equation N = 2 P to find N .$	$N = 2 \times 15 = 30$

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C

Emily and Jack are preparing supplies for a workshop. Emily thinks that the number of notebooks should be twice the number of pens, so N = 2 P, while Jack thinks that the number of pens should be 5 more than one-third of the number of notebooks, so P = \frac{1}{3} N + 5 . How many notebooks should they prepare so that Emily and Jack can agree on the number of pens to prepare?

Explanation	Calculations	Help
$We first create variables to represent the number of notebooks and pens.$	$N = number of notebooks P = number of pens$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate Emily's statement "the number of notebooks should be twice the number of pens" into an equation.$	$N = 2 P$	Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate Jack's statement "the number of pens should be 5 more than one-third of the number of notebooks" into an equation.$	$P = \frac{1}{3} N + 5$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS2-B Click to view full details
$We substitute the expression for N from Emily's equation into Jack's equation to write it in terms of P .$	$P = \frac{1}{3} (2 P) + 5$
$We simplify the right side by multiplying the fraction.$	$P = \frac{2}{3} P + 5$
$We subtract \frac{2}{3} P from both sides to group like terms.$	$P - \frac{2}{3} P = 5$	Theory & Tactics Method Card EQUA1-B Click to view full details
$We simplify the left side and then divide both sides by \frac{1}{3} to solve for P .$	$\frac{1}{3} P = 5 P = 5 \times 3 = 15$	Theory & Tactics Method Card EQUA1-C Click to view full details
$We substitute P = 15 into the equation N = 2 P to find N .$	$N = 2 \times 15 = 30$

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C