Tom spent 1/5 of his money and 1/4 of the remainder on a magazine. He had $25.80 left. How much was the magazine?
A $5.10
B $6.45
C $8.60
D $7.80
he spent 1/4 of the remainder on the magazine
25.80 was 3/4 of the remainder
So, the magazine was 1/3 of 25.80 = 8.60
To find out how much the magazine cost, we need to work backwards from the information given.
Let's first find out how much money Tom had before spending any. We know that he had $25.80 left after making his purchases.
Let's assume that the amount Tom had left after spending 1/5 of his money is X.
So, 1/5 of Tom's money = X
After spending 1/5 of his money, Tom had 4/5 of his money remaining.
Therefore, 4/5 of Tom's money = $25.80
To find the original amount Tom had, we need to determine the value of 1/5 (X) that we calculated earlier. We can do this by multiplying $25.80 by the reciprocal of 4/5, which is 5/4.
Original amount of money Tom had = $25.80 × (5/4) = $32.25
Now, we know that Tom spent 1/4 of the remainder on a magazine, which means he had 3/4 of the remainder left after buying the magazine.
Let's assume the cost of the magazine is M.
Therefore, 3/4 of the remainder = $25.80 - M
We can now set up an equation to solve for M:
3/4 of (original amount of money - amount spent on magazine) = $25.80 - M
Substituting the value of the original amount of money Tom had, we get:
3/4 × $32.25 = $25.80 - M
Simplifying this equation, we get:
$24.19 = $25.80 - M
Now, let's solve for M by moving the terms around:
$24.19 + M = $25.80
Subtracting $24.19 from both sides, we get:
M = $25.80 - $24.19
Calculating the value, we find:
M = $1.61
Therefore, the cost of the magazine is $1.61.
The correct answer is not among the provided options. The closest option is $1.61, which is not listed. Therefore, none of the options provided match the correct answer.