GMAT Practice Question: 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 ?
- 2 x-49
- 2 x+49
- 2 x-65
- 49-2 x
- 65-2 x
Topics: word problems, linear equations, expression formulas, translations
Solution
Step 1
We first create non-ambiguous variables for each coin type.
x = \text{number of dimes} n = \text{number of nickels} q = \text{number of quarters}
Step 2
We translate the relative comparison \textbf{\text{"8 more nickels than dimes"}} into a mathematical expression.
n = x + 8
Step 3
We translate the total count statement \textbf{\text{"A purse contains 57 coins"}} into an equation for the sum of the coins.
x + n + q = 57
Step 4
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
Answer
The number of quarters in terms of x is 49 - 2x, corresponding to choice D.
