The first month's dues will be used to rent a film about computer-related careers, to purchase a reference book, and to buy refreshments for the next meeting. If 1/2 of the money is spent on her film, 1/4 of the remainder is used for refreshments, and $7.50 is spent on the book, how much money will be spent?
.5 x for film , .5 x left
.25 * .5 x = .125 x on refreshments so
.5 x - .125 x = .375 left for the book
so
.375 x = 7.50
x = 20 dollars
Let's assume the first month's dues amount to x dollars.
1/2 of the money is spent on the film, so the amount spent on the film is (1/2) * x = x/2 dollars.
The remainder of the money after buying the film is (x - x/2) = (1/2) * x = x/2 dollars.
1/4 of the remainder is used for refreshments, so the amount spent on refreshments is (1/4) * (x/2) = x/8 dollars.
$7.50 is spent on the book.
Adding up the amounts spent: x/2 + x/8 + $7.50.
To simplify, we need to find the common denominator for x/2 and x/8, which is 8.
(x/2) * (4/4) = (4x/8) dollars.
(x/8) dollars + (4x/8) dollars + $7.50.
Combining the fractions: (4x/8) + (x/8) = (5x/8).
Therefore, the total amount spent is (5x/8) + $7.50.
Since we don't have a specific value for x, we can't determine the exact amount spent.
To solve this problem, we need to break it down step by step.
Step 1: Calculate the amount of money spent on the film.
Given that half of the money is spent on the film, we can say that 1/2 * x represents the amount spent on the film, where x is the total amount of money.
Thus, the amount spent on the film is (1/2) * x.
Step 2: Calculate the remainder after spending on the film.
To find the remainder after spending on the film, we subtract the amount spent on the film from the total amount of money.
So, the remainder is x - (1/2) * x = (1/2) * x.
Step 3: Calculate the amount spent on refreshments.
Given that 1/4 of the remainder is spent on refreshments, we can say that (1/4) * (1/2) * x represents the amount spent on refreshments.
Thus, the amount spent on refreshments is (1/4) * (1/2) * x.
Step 4: Calculate the remainder after spending on refreshments.
To find the remainder after spending on refreshments, we subtract the amount spent on refreshments from the remainder calculated in step 2.
So, the remainder after spending on refreshments is (1/2) * x - (1/4) * (1/2) * x = (1/2) * x - (1/8) * x.
Step 5: Subtract the amount spent on the book.
From the remainder after spending on refreshments (calculated in step 4), we subtract the amount spent on the book, which is $7.50.
So, the final amount of money spent is [(1/2) * x - (1/8) * x] - $7.50.
To determine the exact amount of money spent, we need the value of x (the total amount of money). This information is missing, so it's not possible to provide an exact answer to the question without that information.