Josh has some money. He uses 5/8 of his money to buy 10 cakes. With the rest of the money, he can buy 3 cakes and 9 cookies. A cake costs $4.50 more than a cookie. How much money did he spend on cakes?
Let Josh has 8x dollars
Because he uses 5/8 of his money to buy 10 cakes.
5/8 * 8x = 5x dollars can buy 10 cakes
So a cake is 5 * 10 = 0.5x dollars
A cake costs $4.50 more than a cookie
So a cookie is 0.5x - 4.50 dollars
The rest of the money is 8x - 5x = 3x dollars
With the rest of the money, he can buy 3 cupcakes and 9 cookies
So 3x = 3 * (0.5x) + 9 (0.5x - 4.50)
3x = 1.5x + 4.5x - 40.5
3x = 6x - 40.5
-3x = -40.5
x = 13.5
So a cake is 0.5x = 0.5 * 13.5 = 6.75 dollars
Josh buy 10 + 3 = 13 cakes in total
So he spent 13 * 6.75 = 87.75 dollars on cakes
Let's assume that the total amount of money Josh has is x dollars.
He uses 5/8 of his money to buy 10 cakes, so the amount of money he spends on cakes can be calculated by (5/8) * x.
The remaining amount of money can be calculated as x - (5/8) * x.
With the rest of the money, he can buy 3 cakes and 9 cookies. The cost of one cake is $4.50 more than a cookie, which means each cake costs the same as a cookie plus $4.50.
Let's assign the cost of a cookie as c dollars. Therefore, the cost of a cake is (c + $4.50) dollars.
The total cost of 3 cakes is 3 * (c + $4.50) dollars.
The remaining amount of money after buying the cakes can be represented as x - (5/8) * x.
According to the given information, the remaining amount of money after buying the cakes is equal to the cost of 3 cakes plus 9 cookies, so we have the equation:
x - (5/8) * x = 3 * (c + $4.50) + 9 * c
To solve the equation, we need to find the value of c.
To find out how much money Josh spent on cakes, we need to calculate the total cost of the cakes.
Let's first determine the cost of a cake and a cookie. We're given that a cake costs $4.50 more than a cookie. Let's say the cost of a cookie is C dollars, then the cost of a cake would be C + $4.50.
Next, we need to find out how much money Josh spent on cakes. We're told that he used 5/8 of his money to buy 10 cakes. This means that the remaining 3/8 of his money was used to buy 3 cakes and 9 cookies.
Let's assume that Josh's total money is M dollars. Then, Josh spent 5/8 * M on buying cakes, and the remaining 3/8 * M was used to buy 3 cakes and 9 cookies.
According to the given information, 3/8 * M can buy 3 cakes and 9 cookies. Since a cake costs C + $4.50 and a cookie costs C dollars, the total cost of the 3 cakes and 9 cookies would be:
3 * (C + $4.50) + 9 * C
Now, we need to find the value of C. To do this, we can compare the cost of the cakes to the cost of the 3 cakes and 9 cookies:
5/8 * M = 3 * (C + $4.50) + 9 * C
Simplifying the equation further, we have:
5/8 * M = 3C + $13.50 + 9C
Combining like terms, we get:
5/8 * M = 12C + $13.50
We can now solve for C:
5M = 96C + $108
Dividing both sides by 96, we have:
5/96M = C + $1.125
Now that we know the value of C, we can determine the cost of the cakes:
Cost of cakes = 10 * (C + $4.50)
Calculating this expression will give us the amount of money Josh spent on cakes.