Darrell spent half of his money on a dictionary. He spent half of the remaining money on some storybooks. After spending $6 on a fast food meal, he was left with $10. How much did Darrell have at first?
.5M - .25M - 6 = 10
Solve for M.
Well, it seems like Darrell's budget was a real page-turner! Let's do some detective work to solve this riddle.
Darrell started with an amount of money, and then he spent half of it on a dictionary. That means he had another half left. But we don't know how much that is yet, so let's call it X.
After buying the dictionary, Darrell spent half of the remaining X on storybooks. That means he had 1/2 * X = X/2 left.
Now, subtracting the $6 he spent on a fast food meal from his X/2, we can set up the following equation:
X/2 - 6 = 10
Solving for X, we can multiply both sides by 2 to get rid of that pesky fraction:
X - 12 = 20
Adding 12 to both sides, we uncover the value of X:
X = 32
So, it looks like Darrell had $32 at first! He could have bought a whole library with that kind of dough!
Let's work step by step to find out how much Darrell had at first.
Step 1: Darrell spent half of his money on a dictionary
Let's assume the initial amount of money Darrell had as "X".
Darrell spent half of his money on a dictionary, so he spent X/2 on a dictionary.
Step 2: He spent half of the remaining money on some storybooks.
After buying the dictionary, the remaining amount of money is X/2.
He spent half of the remaining money on storybooks, so he spent (X/2)/2 = X/4 on storybooks.
Step 3: After spending $6 on a fast food meal, he was left with $10.
After spending $6 on a fast food meal, the remaining amount of money is $10.
So, the equation can be formed as:
(X/2) - (X/4) - $6 = $10
Simplifying the equation:
2*(X/2) - (X/4) - $6 = $10
X - (X/4) - $6 = $10
Multiplying everything by 4 to eliminate the fraction:
4X - X - $24 = $40
3X = $64
X = $64/3
Therefore, Darrell had $64/3 at first.
To find out how much Darrell had at first, let's break down the information given step by step:
1. Darrell spent half of his money on a dictionary.
- Let's call the amount of money Darrell had at first "x."
- After spending half of his money on a dictionary, he would have (x/2) dollars remaining.
2. Darrell spent half of the remaining money on some storybooks.
- After buying the dictionary, Darrell had (x/2) dollars left.
- He spent half of that amount on storybooks, which is (1/2) * (x/2) = x/4 dollars.
3. After spending $6 on a fast food meal, Darrell was left with $10.
- The amount of money Darrell had after buying the dictionary and storybooks is (x/2 - x/4) = x/4 dollars.
- After spending $6 on a fast food meal, Darrell was left with (x/4 - 6) dollars, which equals $10.
Now, we can set up the equation and solve for "x":
x/4 - 6 = 10
To isolate x, we can add 6 to both sides of the equation:
x/4 = 16
Finally, multiply both sides of the equation by 4 to solve for x:
x = 16 * 4
x = 64
Therefore, Darrell had $64 at first.