Mary bought a scarf for five dollar spent Half of the remaining money on jogging shoes bought lunch for two dollars and then spent half of her remaining dollars on a DVD she had $10 left how much money does she start with?
starting amount ---- x
spent $5, amount left = x-5
after spending half of that on jogging shoes,
amount left = (1/)(x-5)
after spending $2 for lunch, amount left
= (1/2)(x-5) - 2
spent half of that on a DVD, amount left
= (1/2)[(1/2)(x-5) - 2] which equals 10
(1/2)(x-5) - 2 = 20
(1/2)(x-5) = 22
x-5 = 44
x = $49
check:
start with 49
spent $5 on scarg, amount left = 44
spent half, amount left = 22
spent $2 on lunch, amount left = 20
spent half of that on DVD, amount left = 10
Mary is quite the savvy spender! Let's do some mathemagics to figure out how much money she started with.
So, Mary bought a scarf for $5, which means she had some money before that. After buying the scarf, she spent half of her remaining money on jogging shoes, which brings us to the point of SherlockBot-ing.
If she had $10 left after buying the DVD, then half of her remaining money before buying the DVD must have been $20. And half of her money before buying lunch must have been $40.
So, drumroll please... Mary started with a whopping $40 in her pocket! Now that's some serious cash-flow!
Let's break it down step-by-step:
1. Mary bought a scarf for $5.
2. She spent half of the remaining money on jogging shoes.
- Since she had $10 left after buying the DVD, the amount spent on jogging shoes is $10.
3. Mary then bought lunch for $2.
- This means her remaining money before buying lunch is $10 + $2 = $12.
4. She spent half of the remaining dollars on a DVD.
- After buying the DVD, she had $10 left. This means she spent $12 - $10 = $2 on the DVD.
5. Lastly, we need to calculate how much money Mary started with.
- Before buying lunch, she had $12. Before buying the DVD, she had $12 + $2 = $14. And before buying the scarf, she had $14 + $5 = $19.
Therefore, Mary started with $19.
To solve this problem, we can work backwards and determine the amounts at each step.
Let's denote the initial amount of money Mary had as "x" dollars.
1. Mary bought a scarf for five dollars: This means she had (x - 5) dollars remaining.
2. She then spent half of the remaining money on jogging shoes: Therefore, she spent (1/2)(x - 5) dollars. Thus, she had (x - 5) - (1/2)(x - 5) dollars left.
3. Next, Mary bought lunch for two dollars: This means she spent an additional 2 dollars. Thus, she had [(x - 5) - (1/2)(x - 5)] - 2 dollars left.
4. Finally, Mary spent half of her remaining dollars on a DVD and had 10 dollars left: This means she spent (1/2)[(x - 5) - (1/2)(x - 5) - 2] dollars. Therefore, we can set up the equation:
[(x - 5) - (1/2)(x - 5) - 2] - (1/2)[(x - 5) - (1/2)(x - 5) - 2] = 10
Now, we can solve for x:
[(x - 5) - (1/2)(x - 5) - 2] - (1/2)[(x - 5) - (1/2)(x - 5) - 2] = 10
Simplify the equation by combining like terms:
[(x - 5) - (1/2)(x - 5) - 2] - 1/2[(x - 5) - (1/2)(x - 5) - 2] = 10
Simplify further:
[(x - 5) - (1/2)(x - 5) - 2] - [(1/2)(x - 5) - (1/4)(x - 5) - 1] = 10
Continue simplification:
[x - 5 - (1/2)x + 5/2 - 2] - [1/2x - 5/2 - 1/4x + 5/4 - 1] = 10
Group like terms:
[x - (1/2)x - 1/4x] + [5/2 - 2 - 5/2 + 5/4 - 1] = 10
Combine like terms:
[(4/4)x - (2/4)x - (1/4)x] + [0] = 10
Simplify:
[(1/4)x] = 10
Multiply both sides by 4:
x = 10 * 4
x = 40
Therefore, Mary started with 40 dollars.