Problem Solving

Vincen wrote: ↑

Sun Feb 14, 2021 11:34 am

Mark has in his safe $100 and $50 notes that when added give a total of 36 notes. If the $100 notes were to be changed by $50 notes and the $50 notes by $100 notes Mark would have a total of 42 notes. How many $50 notes does Mark have?

A) 16
B) 18
C) 20
D) 24
E) 36

Answer: C

Source: e-GMAT

Solution:

We can let x be the number of $100 notes and y be the number of $50 notes; thus, we can create the equation:

x + y = 36

When the $100 notes are replaced by $50 notes, to maintain the total value of the $100 notes, we need twice as many $50 notes. Similarly, when the $50 notes are replaced by $100 notes, to maintain the total value of the $50 notes, we need half as many $100 notes. That is, we have:

2x + y/2 = 42

Multiplying the first equation by 2 (and obtaining 2x + 2y = 72) and subtracting the second equation from that, we have:

3y/2 = 30

y = 20

Answer: C