Alexander B. answered • 09/12/15

Advanced Math and Science Tutoring and Test Prep online (SAT, ACT)

Hello Gretchen,

Here's the possible solution. First, write all the constraints pertinent to the case:

x1+x2+x3+x4=30

all numbers must be even

x2+x3+x4<15

x2+x3+x4<15

where variables: x1, x2, x3 and x4 stand for the original amounts in envelopes, x1 containing the largest amount.

Based on these constraints, there are only 2 possible combinations. The 1st one:

**before: x1=16, x2=8, x3=4, x4=2**

**after: x1=2, x2=16, x3=8, x4=4**

**thus, this is the correct answer because numbers are the same, only in different order**

2nd combination of numbers does not satisfy the conditions (discard)

before: x1=18, x2=6, x3=4, x4=2

after: x1=6, x2=12, x3=8, x4=4 - discard

before: x1=18, x2=6, x3=4, x4=2

after: x1=6, x2=12, x3=8, x4=4 - discard

Hope this will help.