Question

Austin's farm picked a total of 340 pumpkins. Austin separated the pumpkins into small and large. He sold the small pumpkins for $3 each and the large ones for $8 each. He sold all of the pumpkins for a total of $2120. How many small and large pumpkins did Austin originally pick? Solve for x and y.

Answer 1

Austin originally picked 120 small pumpkins and 220 large pumpkins.

Step-by-step explanation:

Let x be the number of small pumpkins and y be the number of large pumpkins.

According to the given information, we can set up two equations:

x + y = 340 (equation 1)

3x + 8y = 2120 (equation 2)

Now we can solve this system of equations.

We can multiply equation 1 by 3 to eliminate the x variable: 3(x + y) = 3(340), which simplifies to 3x + 3y = 1020.

Next, we subtract equation 2 from the modified equation to eliminate the x variable:

(3x + 3y) - (3x + 8y) = 1020 - 2120

This simplifies to -5y = -1100.

Dividing both sides of the equation by -5, we get y = 220.

Now we substitute the value of y in equation 1 to solve for x:

x + 220 = 340

Subtracting 220 from both sides of the equation, we get x = 120.

Therefore, Austin originally picked 120 small pumpkins and 220 large pumpkins.