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.