Problem Solving

BTGModeratorVI wrote: ↑

Thu Nov 05, 2020 8:02 am

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?

А. 12
B. 16
C. 20
D. 24
E. 48

Answer: E
Source: Official guide

Let S = the number of sandwiches to order
Let P = the number of pastries to order

David thinks that there should be twice as many sandwiches as there are pastries
In other words, the number of sandwiches is twice the number of pastries
We can write: S = 2P

Ron thinks the number of pastries should be 12 more than one-fourth of the number of sandwiches.
We can write: P = S/4 + 12

How many sandwiches should be ordered so that David and Ron can agree on the number of pastries to order?
We now have the following system:
S = 2P
P = S/4 + 12

Take the top equation and replace P with S/4 + 12 to get: S = 2(S/4 + 12)
Simplify: S = S/2 + 24
Multiply both sides of the equation by 2 to get: 2S = S + 48
Subtract S from both sides to get: S = 48

Answer: E

Cheers,
Brent