There are two ways of solving this problem - one by using algebra, the other by trial and error. The trial and error method can easily take a very long time to figure out. Your teacher probably wants it done by using algebra
ALGEBRA METHOD:
START BY WRITING YOUR KNOWNS
Total=$10,000
Let x=Amount received by Joe
So x+$3,000 = Amount received by Jane= x+$3,000
According to the problem, there is a total of $10,000. That's what the amounts received by Joe AND Jane will equal. So your equation will be equal to $10,0000. We need to add together the amounts received by Joe and Jane in order to get the total. So your equation looks like this:
x+x+$3,000=$10,000 Combine like terms
2x+3,000=10,000 I dropped the $ for clarity
2x3,000-3,000=10,000-3,000 Subtract the constant ($3,000) from each side
2x=7,000
2x/2=7,000/2 Divide each side by the coefficient (2)
x=3,500
Joe receives 3,500
Jane receives 3,000 more, or 6,500
Check: Always check your answer by plugging your answers back into the original problem
3,500+6,500=10,0000
TRIAL AND ERROR METHOD
-If Joe and Jane each received the same, they would receive 5000 each because 10,000 divided by 2 is 5,000.
-Now we have to go by trial and error until the two numbers equal 10,000 and one is 3,000 more than the other.
-I'm going to try to take away 1,000 from one and give it to the other. Now one number is 4,000 and the other is 6,000. Added together they equal 10,000. But they are only 2,000 apart.
-I'm going to try it again and take away 1,000 from one and give it to the other. Now one number is 3,000 and the other is 7,000. They still equal 10,000 but now they're 4,000 apart. So I've taken away too much.
-I'm going to go back to 4,000 and 6,000.
-Instead of taking away 1,000, I'm going to try 100. Now one number is 3,900 and the other is 6,100. Equal 10,000 but still not 3,000 apart.
-In order to find the answer, you would have to keep taking guesses and trying them out until you found the right combination. DEFINITELY NOT THE FASTEST OR EASIEST WAY TO SOLVE THIS PROBLEM!
