Mrs. Daniel pays $324 for a handbag and 3 pairs of shoes. The handbag cost half as much as the 3 pairs of shoes combined. Find the cost of the hand bag.
cost of 3 pairs of shoes ---- x
cost of handbag ---------- (1/2)x or x/2
x + x/2 = 324
times 2
2x + x = 648
3x = 648
x = 216
The 3 pairs of shoes cost $216 and the handbag cost $108
I set up as an equation:
(1/2)*x*3 = 324
solving for x will give you the total cost of the three pairs of shoes
x=208
324-216 = 108
hand bag is $108
Let's assume the cost of the handbag is x dollars.
Since the handbag cost half as much as the 3 pairs of shoes combined, the cost of the shoes is 2x dollars.
The total cost of the handbag and the 3 pairs of shoes is $324, so we can set up the equation:
x + 3(2x) = 324
Simplifying the equation:
x + 6x = 324
Combining like terms:
7x = 324
Dividing both sides by 7 to solve for x:
x = 324 / 7 = 46.29
Therefore, the cost of the handbag is approximately $46.29.
To find the cost of the handbag, we need to set up an equation based on the given information.
Let's denote the cost of the handbag as "H" and the cost of each pair of shoes as "S". We can use the given information to write the following equation:
H + 3S = 324 (Equation 1)
The problem states that the handbag cost half as much as the 3 pairs of shoes combined. Mathematically, this can be written as:
H = (1/2)(3S) (Equation 2)
Now we can solve the system of equations by substituting Equation 2 into Equation 1:
(1/2)(3S) + 3S = 324
Simplifying the equation:
3S/2 + 6S/2 = 324
Combining like terms:
9S/2 = 324
To further solve for S, multiply both sides of the equation by 2/9:
S = (2/9) * 324
S = 72
Now we can substitute the value of S back into Equation 2 to find the cost of the handbag:
H = (1/2)(3S)
H = (1/2)(3*72)
H = (1/2)(216)
H = 108
Therefore, the cost of the handbag is $108.