Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks and how many spoons did they make last April?
Let's say that the store made x forks and y spoons last April. The total cost of the materials for the forks is 1.7x, and the total cost of the materials for the spoons is 1.3y.
We also know that the store sold the forks for 5.6x and the spoons for 5.4y.
The total cost of the materials is $37.90, so we have the equation 1.7x + 1.3y = 37.90.
The store sold the forks and spoons for a total of $147.20, so we have the equation 5.6x + 5.4y = 147.20.
We'll solve this system of equations using the substitution method.
Let's solve the first equation for x: x = (37.90 - 1.3y) / 1.7.
Now substitute this x value into the second equation: 5.6 * ((37.90 - 1.3y) / 1.7) + 5.4y = 147.20.
Now we can solve for y.
Multiply both sides of the equation by 1.7 to get rid of the fraction: 5.6 * (37.90 - 1.3y) + 9.18y = 250.24.
Now distribute: 211.84 - 7.28y + 9.18y = 250.24.
Combine like terms: 1.9y + 211.84 = 250.24.
Subtract 211.84 from both sides: 1.9y = 38.40.
Finally, divide both sides by 1.9: y = 38.40 / 1.9 = 20.
Now that we know y, we can substitute it back into the first equation to solve for x.
x = (37.90 - 1.3y) / 1.7 = (37.90 - 1.3 * 20) / 1.7 = (37.90 - 26) / 1.7 = 68 / 1.7 = 40.
Thus, the store made 40 forks and 20 spoons last April. Answer: \boxed{40, 20}.