David and Ron are ordering food for a business lunch. David thinks that there should be twice as...

Question

David and Ron are ordering food for a business lunch. David thinks that there should be twice as many sandwiches as there are pastries, but Ron thinks the number of pastries should be 12 more than one-fourth of the number of sandwiches. How many sandwiches should be ordered so that David and Ron can agree on the number of pastries to order?

GMAT Panda · Accepted Answer

48 sandwiches We first create variables to represent the number of sandwiches and pastries. S =number of sandwiches P = number of pastries We translate David's statement "twice as many sandwiches as there are pastries" into an equation. S = 2P We translate Ron's statement "number of pastries should be 12 more than one-fourth of the number of sandwiches" into an equation. P = 1/4S + 12 We substitute the expression for S from David's equation into Ron's equation to write it in terms of P. P = 1/4(2P) + 12 We subtract 1/2P from both sides to group like terms. P - 1/2P = 12 We divide both sides by 1/2 to solve for P. 1/2P = 12 P = 121/2 = 12 2 = 24 We substitute P = 24 into the equation S = 2P to find S. S = 2 24 = 48

Explanation	Calculations	Help
$We first create variables to represent the number of sandwiches and pastries.$	$S = number of sandwiches P = number of pastries$
$We translate David's statement "twice as many sandwiches as there are pastries" into an equation.$	$S = 2 P$
$We translate Ron's statement "number of pastries should be 12 more than one-fourth of the number of sandwiches" into an equation.$	$P = \frac{1}{4} S + 12$
$We substitute the expression for S from David's equation into Ron's equation to write it in terms of P .$	$P = \frac{1}{4} (2 P) + 12$
$We subtract \frac{1}{2} P from both sides to group like terms.$	$P - \frac{1}{2} P = 12$
$We divide both sides by \frac{1}{2} to solve for P .$	$\frac{1}{2} P = 12 P = \frac{12}{\frac{1}{2}} = 12 \times 2 = 24$
$We substitute P = 24 into the equation S = 2 P to find S .$	$S = 2 \times 24 = 48$

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