Mrs. Daniels 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
cost of handbag ---- x
cost of 3 pairs of shoes ---- y
we are told "handbag costs 1/2 of cost of shoes
x = (1/2)y
and x+y = 324
(1/2)y + y = 324
1.5y = 324
y = 216
x = 108
handbag costs $108
108
To find the cost of the handbag, we need to set up an equation based on the given information.
Let's say the cost of the handbag is 'x' dollars. According to the problem, the handbag costs half as much as the 3 pairs of shoes combined.
The cost of the 3 pairs of shoes is $324 - the total price Ms. Daniels paid. Let's call the cost of the 3 pairs of shoes 'y' dollars.
From the problem, we know that:
x = y/2
We also know that the total cost of the handbag and shoes is $324, so:
x + y = 324
Now we have a system of two equations:
x = y/2
x + y = 324
We can solve this system of equations to find the cost of the handbag 'x'.
From the first equation, we can multiply both sides by 2 to get rid of the fraction:
2x = y
Now we can substitute this value of 'y' in the second equation:
x + 2x = 324
3x = 324
Dividing both sides by 3, we find:
x = 108
Therefore, the cost of the handbag is $108.