SOLUTION: One number is 3 less than a second number. Twice the second number is 9 less than 5 times the first. Find the smaller of the two numbers.

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Question 285894: One number is 3 less than a second number. Twice the second number is 9 less than 5 times the first. Find the smaller of the two numbers.
Found 2 solutions by richwmiller, mgmoeab:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
You tried so hard that you put this problem under finance. I am so impressed that I will do all of your homework for the next 20 years.

Answer by mgmoeab(37) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the first number
Let B be the second number
You know that:
- One number is 3 less than a second number. ( A = 3 - B )
- Twice the second number is 9 less than 5 times the first. ( 2B = 9 - 5A)
1).- A = 3 - B
2).- 2B = 9 - 5A
If we substitute (1) in (2), then:
2B = 9 - 5( 3 - B)
2B = 9 - 15 + 5B
-3B = -6
B= 2
Now, we know that the second number (B) is 2, but they are asking you to find the smaller number of the two. This means we need to find A to see which one is the correct answer.
Substituting B =2 in (1):
A = 3 - 2
A = 1
Since 1 < 2, then the correct answer would be: The first number is smaller.