Question

Fred and George are working on selling their magical items in the common room. Fred sold 8 Whiz Bangs and 4 Love Potions for a total of $188. George sold 3 Whiz Bangs and 8 Love Potions for a total of $220. How much was each item?

Options:

A) Whiz Bangs: $15, Love Potions: $20

B) Whiz Bangs: $10, Love Potions: $15

C) Whiz Bangs: $20, Love Potions: $25

D) Whiz Bangs: $25, Love Potions: $30

Answer 1

Each Whiz Bang costs $12 and each Love Potion costs $23.

Step-by-step explanation:

We can solve this problem by setting up a system of equations. Let's denote the price of a Whiz Bang as 'w' and the price of a Love Potion as 'l'.

From the information given, we can set up the following equations:

8w + 4l = 188 (equation 1)

3w + 8l = 220 (equation 2)

To solve this system, we can use the method of substitution:

Solving equation 1 for 'w', we get:

w = (188 - 4l) / 8.

Substituting this value of 'w' into equation 2, we get:

3((188 - 4l) / 8) + 8l = 220.

Simplifying this equation gives us:

564 - 12l + 64l = 1760.

Combining like terms, we have:

52l = 1196.

Dividing both sides by 52 gives us:

l = 23.

Substituting this value of 'l' into equation 1, we can find the value of 'w':

8w + 4(23) = 188.

Simplifying this equation gives us:

8w + 92 = 188.

Subtracting 92 from both sides, we get:

8w = 96.

Dividing both sides by 8 gives us:

w = 12.

Therefore, each Whiz Bang costs $12 and each Love Potion costs $23.