Great 125

Four different positive whole numbers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, multiply the third by four, and divide the last by four, you will produce four equivalent numbers. What is the greatest of these four numbers?
Source: mathcontest.olemiss.edu 10/14/29013

SOLUTION
Let a,b,c,d represent the four whole numbers. We have the following conditions:
a+b+c+d=125\qquad\left (1\right )
a+4=b-4=4c=\dfrac{d}{4}\qquad\left (2\right)
We use the method of substitution to solve Eq. (1) for c.
Add 4 to both sides of Eq. \left (1\right )
\left (a+4\right )+b+c+d=125+4
Substitute the value of a+4=4c from Eq. \left (2\right )
4c+b+c+d=125+4
Subtract 4 from both sides
4c+\left (b-4\right )+c+d=125+4-4
Substitute the value of b-4=4c
4c+4c+c+d=125
Substitute the value of d=16c
4c+4c+c+16c=125
Simplify
25c=125
c=5
Calculate a
a+4=4c=20
Calculate b
b-4=4c=20
b=24
Calculate d
d=16c=180 the greatest of the four numbers.

Answer: 80

Advertisements

About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s