Darrell spent half of his 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?
Having spent 1/2 + 1/4 = 3/4, he was left with 1/4 of his money. So,
1/4 x - 6 = 10
Let's break down the problem step-by-step:
1. Darrell spent half of his dictionary.
Let's assume Darrell had x dollars at first. He spent half of it, which is x/2.
2. He spent half of the remaining money on some storybooks.
After spending half of his money on storybooks, he had (x/2)/2 = x/4 dollars left.
3. After spending $6 on a fast food meal, he was left with $10.
The remaining money after spending $6 on a fast food meal is x/4 - 6.
According to the problem, x/4 - 6 = $10.
To find the value of x, we can solve the equation:
x/4 - 6 = 10
x/4 = 10 + 6
x/4 = 16
To solve for x, we multiply both sides of the equation by 4:
x = 16 * 4
x = 64
So, Darrell had $64 at first.
To find out how much Darrell had at first, we can work backwards.
Let's start with the amount of money Darrell had left after spending $6 on a fast food meal. We know that he was left with $10, so his remaining money can be represented by the equation:
Remaining money = Total money - Spent on fast food meal
$10 = Total money - $6
We can solve this equation by isolating the "Total money" variable:
Total money = $10 + $6
Total money = $16
Now, let's figure out how much money Darrell spent on storybooks. We know that he spent half of the remaining money, which is $16. So his spending on storybooks can be represented by the equation:
Spending on storybooks = (1/2) * Remaining money
Spending on storybooks = (1/2) * $16
Spending on storybooks = $8
Finally, let's find out how much money Darrell had at the beginning. We know that he spent half of his dictionary and half of the remaining money. So his initial amount of money can be represented by the equation:
Initial amount of money = Remaining money + Spending on storybooks + Spent on fast food meal
Initial amount of money = $16 + $8 + $6
Initial amount of money = $30
Therefore, Darrell had $30 at first.