a store sells homemade forks and spoons. the store sells homemade forks for $5.50 each and the homemade spoons for $3.50 each. last month the store sold a total of 61 homemade spoons and forks for $289.50. How many were homemade forks and how many where homemade spoons?

Let's denote the number of homemade forks as x and the number of homemade spoons as y .

From the problem, we can create the following system of equations:

1. The total number of homemade forks and spoons is 61:
x + y = 61

2. The total cost of all forks and spoons is $289.50:
5.50x + 3.50y = 289.50

We can use the first equation to express x in terms of y :
x = 61 - y

Substitute this expression for x into the second equation:
5.50(61 - y) + 3.50y = 289.50

Now, solve for y :
335.50 - 5.50y + 3.50y = 289.50
-2y = -46
y = 23

Now that we have found the number of homemade spoons, we can find the number of homemade forks:
x = 61 - 23
x = 38

Therefore, there were 38 homemade forks and 23 homemade spoons sold.

Answer: There were 38 homemade forks and 23 homemade spoons sold.