Jack and Bill had $440 altogether. Bill had $20 more than Jack. When Jack spent 1/3 the amount of money spent by Bill, he had 3 times as much money as Bill. How much money did Bill spend?
Jack's amount --- x
Bill's amount = x+20
x+x+20 = 440
x = 210
So Jack had 210 and Bill had 230
amount spent by Bill --- y , amount left = 230-y
amount spent by Jack = 1/3 y , amount left = 210 - 1/3 y
210 - y/3 = 3(230-y)
210 - y/3 = 690 - 3y
8y/3 = 480
8y = 1440
y = 180
Bill spent $180
check:
Bill spent 180 leaving him with 50
Jack spent 60 , leaving him with 150
which is 3 times what Bill has left
My answer is correct
Well, well, well, looks like Jack and Bill are in a bit of a financial puzzle. Let's see if Clown Bot can bring some humor into this!
Let's start by playing around with the equations. We know that Bill had $20 more than Jack, so we can write an equation: B = J + $20.
Now, we also know that when Jack spent 1/3 the amount of money spent by Bill, he had 3 times as much money as Bill. Let's break this down into an equation too: J - (1/3)B = 3B.
Now, let's substitute the first equation into the second equation: (J + $20) - (1/3)(J + $20) = 3(J + $20).
Now comes the fun part, let's solve this equation!
(J + $20) - (1/3)(J + $20) = 3(J + $20)
To avoid any crazy decimals, let's multiply everything by 3, and let's do some algebraic magic!
3J + $60 - J - $20 = 9J + $60
Now let's simplify it even further!
2J + $40 = 9J + $60
Subtracting 2J from both sides and subtracting $40 from both sides, we get:
$20 = 7J
Hey, we've discovered a Jack in the money-making business! Jack has $20, which means Bill has $20 + $20 = $40.
Now, let's talk about Bill's spending habits. If Jack spent 1/3 of what Bill did, and Bill has $40, then Jack spent 1/3 * $40 = $<<1/3*40=13.33>>13.33 (rounded to the nearest cent).
So, Bill spent the remainder of the money, which is $40 - $13.33 = $<<40-13.33=26.67>>26.67 (rounded to the nearest cent).
Voila! Bill spent approximately $26.67.
Let's consider the step-by-step approach to solve the problem.
Step 1: Let's assume the amount of money Jack had as 'x'.
Step 2: According to the problem, Bill had $20 more than Jack. So, Bill had 'x + $20'.
Step 3: Together, Jack and Bill had $440. So, we can write the equation:
x + (x + $20) = $440
Step 4: Simplifying the equation, we get:
2x + $20 = $440
2x = $440 - $20
2x = $420
Step 5: Dividing both sides of the equation by 2, we get:
x = $420 / 2
x = $210
Step 6: Now that we know x, we can find the amount of money Bill had:
Bill had x + $20 = $210 + $20 = $230
Therefore, Bill had $230.
Let's break down the problem step by step to find the amount of money Bill spent:
1. Let's assume that Jack had x dollars.
2. According to the problem, Bill had $20 more than Jack, so Bill had (x + $20) dollars.
3. Together, Jack and Bill had $440, so we can write the equation: x + (x + $20) = $440.
4. Simplifying the equation, we get 2x + $20 = $440.
5. Subtracting $20 from both sides, we have 2x = $420.
6. Dividing both sides of the equation by 2, we find x = $210.
7. Now we know that Jack had $210.
8. Jack spent 1/3 the amount of money spent by Bill, which means he spent (1/3) * (x + $20), or ($210 + $20)/3 = $230/3.
9. According to the problem, Jack had 3 times as much money as Bill after he spent this amount. So, we can write the equation: Jack's money after spending = 3 * Bill's money after spending.
10. Jack's money after spending = $210 - $230/3.
11. Bill's money after spending = Bill's money before spending - Jack's money after spending.
12. Setting up the equation, we have 3 * (Bill's money after spending) = $210 - $230/3 - (Bill's money before spending - Bill's money after spending).
13. Simplifying the equation further, we have:
- 3 * (Bill's money after spending) = $630 - $230 - 3 * (Bill's money before spending).
- 3 * (Bill's money after spending) = $400 - 3 * (Bill's money before spending).
14. Combining like terms and rearranging the equation, we get:
- 3 * (Bill's money before spending) + 3 * (Bill's money after spending) = $400.
- 3 * (Bill's money before spending + Bill's money after spending) = $400.
- 3 * Bill's total money = $400.
- Bill's total money = $400 / 3.
15. Therefore, Bill spent his total money minus the money he had before spending: Bill's total money - Bill's money before spending = $400 / 3 - $210.
16. Simplifying the equation, we find Bill spent $400 / 3 - $210.