Francesca brought 27 key chains of two different kinds to make goody bags for her birthday party. Leather key chains were 3$ and beaded were 2$.she spent 73$. How many key chains of each kind did she buy?
Let x be the number of leather key chains and y be the number of beaded key chains.
The total number of key chains is given by x + y = 27. (1)
The total cost of the key chains is given by 3x + 2y = 73. (2)
We can solve this system of equations by first isolating x in equation (1) to get x = 27 - y.
Substitute x = 27 - y into equation (2):
3(27 - y) + 2y = 73
81 - 3y + 2y = 73
-y = -8
y = 8
Now that we have the value of y, we can substitute y = 8 back into x = 27 - y to find x:
x = 27 - 8
x = 19
Francesca bought 19 leather key chains and 8 beaded key chains.