A purse contains 57 coins, all of which are nickels, dimes, or quarters. If the purse contains...

Question

A purse contains 57 coins, all of which are nickels, dimes, or quarters. If the purse contains x dimes and 8 more nickels than dimes, which of the following gives the number of quarters the purse contains in terms of x ?

GMAT Panda · Accepted Answer

The number of quarters in terms of x is 49 - 2x, corresponding to choice D. We first create non-ambiguous variables for each coin type. x = number of dimes n = number of nickels q = number of quarters We translate the relative comparison "8 more nickels than dimes" into a mathematical expression. n = x + 8 We translate the total count statement "A purse contains 57 coins" into an equation for the sum of the coins. x + n + q = 57 We substitute the expression for n into the total and isolate q. x + (x + 8) + q = 57 2x + 8 + q = 57 2x + q = 49 q = 49 - 2x

Explanation	Calculations	Help
$We first create non-ambiguous variables for each coin type.$	$x = number of dimes n = number of nickels q = number of quarters$
$We translate the relative comparison "8 more nickels than dimes" into a mathematical expression.$	$n = x + 8$
$We translate the total count statement "A purse contains 57 coins" into an equation for the sum of the coins.$	$x + n + q = 57$
$We substitute the expression for n into the total and isolate q .$	$x + (x + 8) + q = 57 2 x + 8 + q = 57 2 x + q = 49 q = 49 - 2 x$

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