Mrs. Daniel pays $324 for a handbag and 3 pairs of shoes. The handbag costs half as much as the 3 pairs of shoes combined. Find the cost of the handbag.

Let x = handbag cost

x + 2x(for 3 pr. shoes) = 324

3x = 324

x = ?

108

Let's suppose the cost of the handbag is "x" dollars.

According to the information given, the handbag costs half as much as the 3 pairs of shoes combined.

So, the cost of the 3 pairs of shoes combined is 2x dollars.

The total cost of the handbag and the 3 pairs of shoes is $324.

Therefore, we can write the equation:

x + 2x = 324

Combining like terms, we get:

3x = 324

To solve for x, we divide both sides of the equation by 3:

x = 324 / 3

Simplifying, we find:

x = 108

So, the cost of the handbag is $108.

To find the cost of the handbag, we can set up an equation based on the given information. Let's represent the cost of the handbag as "H" and the cost of one pair of shoes as "S".

According to the problem, the handbag costs half as much as the 3 pairs of shoes combined. So, the cost of the handbag is equal to half of the cost of 3 pairs of shoes.

Let's express this mathematically:
H = (1/2) * (3S)

Now, we know that Mrs. Daniel pays $324 for the handbag and 3 pairs of shoes. We can add the cost of the handbag to the cost of the 3 pairs of shoes and set that equal to $324.

H + 3S = 324

We have two equations now. Let's substitute the value of H from the first equation into the second equation:

(1/2) * (3S) + 3S = 324

Simplifying the equation:
(3/2)S + 3S = 324
(3/2 + 2)S = 324
(7/2)S = 324

To solve for S, we can multiply both sides of the equation by 2/7:
S = (2/7) * 324

Now, we can calculate the cost of the handbag by substituting the value of S back into the first equation:
H = (1/2) * (3S)
H = (1/2) * (3 * (2/7) * 324)

Simplifying the equation further:
H = (1/2) * ((6/7) * 324)
H = (3/7) * 324

Calculating the value:
H = (3/7) * 324 = 972/7 ≈ 138.86

Therefore, the cost of the handbag is approximately $138.86.