GMAT Practice Question: 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?
- 12
- 16
- 20
- 24
- 48
Topics: linear equations, word problems, translations
Solution
Step 1
We first create variables to represent the number of sandwiches and pastries.
S =\text{number of sandwiches} P = \text{number of pastries}
Step 2
We translate David's statement \textbf{\text{"twice as many sandwiches as there are pastries"}} into an equation.
S = 2P
Step 3
We translate Ron's statement \textbf{\text{"number of pastries should be 12 more than one-fourth of the number of sandwiches"}} into an equation.
P = \frac{1}{4}S + 12
Step 4
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}(2P) + 12
Step 5
We subtract \frac{1}{2}P from both sides to group like terms.
P - \frac{1}{2}P = 12
Step 6
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
Step 7
We substitute P = 24 into the equation S = 2P to find S.
S = 2 \times 24 = 48
Answer
48 sandwiches
