Bessy has 6 times as much as Bob, but when each earns $6, Bessy will have 3 times as much money as Bob. How much does each have before and after earning the $6? How do you set up the equation?
x=Bessy
y=Bob
x=6y (Bessy has 6 times as much as Bob)
x+6=3(y+6) (when each earns $6, Bessy will have 3 times as much money as Bob)
Solve for x and y
To solve this problem, we can set up equations based on the given information.
Let's start by assigning variables to the amounts of money Bessy and Bob have initially. Let's say Bessy has B dollars and Bob has R dollars.
According to the problem, Bessy has 6 times as much as Bob, so we can create the equation: B = 6R.
We are also told that when each of them earns $6, Bessy will have 3 times as much money as Bob. To represent this, we can set up the equation: B + 6 = 3(R + 6).
Let's solve these equations to find the amount of money each person has initially (before earning $6), as well as after earning $6.
1. Substituting B = 6R in the second equation:
6R + 6 = 3(R + 6)
Now, let's simplify this equation:
6R + 6 = 3R + 18
2. Subtracting 3R from both sides of the equation:
6R - 3R + 6 = 3R - 3R + 18
3R + 6 = 18
3. Subtracting 6 from both sides of the equation:
3R + 6 - 6 = 18 - 6
3R = 12
4. Dividing both sides of the equation by 3:
3R/3 = 12/3
R = 4
Now we have Bob's initial amount: R = 4.
To find Bessy's initial amount, we can substitute R = 4 into the first equation B = 6R:
B = 6(4)
B = 24
So, initially, Bessy has $24 and Bob has $4.
To find the amounts after each person earns $6, we can substitute B = 24 and R = 4 into the equation B + 6 = 3(R + 6):
24 + 6 = 3(4 + 6)
30 = 3(10)
30 = 30
After earning $6, both Bessy and Bob will each have $30.
To summarize:
Initially, Bessy has $24 and Bob has $4. After earning $6, both Bessy and Bob will have $30.