Question

A magician has 60 items in his magical hat. There are 2 quarters for every wand. How many quarters are in his hat?

a. There are 30 quarters in his hat.
b. There are 20 quarters in his hat.
c. There are 15 quarters in his hat.
d. There are 40 quarters in his hat.

Answer 1

By setting up an equation based on the ratio of quarters to wands and the total number of items in the magician's hat, we determined that there are 40 quarters in the hat.

Step-by-step explanation:

The question is about determining the number of quarters in the magician's hat given the ratio of quarters to wands. For every wand, there are 2 quarters. Hence, we can let the number of wands be represented as w, and the number of quarters will be 2w. We know that the total number of items in the hat is 60, which is the sum of the number of wands and the number of quarters. This relationship can be expressed as:

w + 2w = 60

Combining the terms, we have:

3w = 60

To find the value of w, we divide both sides of the equation by 3:

w = 60 / 3

w = 20

Now that we know the number of wands is 20, we can find the number of quarters by multiplying the number of wands by 2:

Quarters = 2 w

Quarters = 2 * 20

Quarters = 40

Therefore, the answer is (d) There are 40 quarters in his hat.