Word problem

Question

a basketball team scored a total of 1470 points over the course of its 21-game season. 470 of the points were from 1 points baskets. The remaining points were either 2 point or 3 point baskets. There were 440 2 points or 3 point baskets scored. How many of those 440 baskets were 3 point baskets?

Answer 1

To solve this you'll want to set up a system of equations.

 

Since there were 1470 points scored total, and 470 of them were from 1 point baskets, that means 1470-470 = 1000 points were scored by 2 and 3 point baskets. Assuming x = the number of 2 point baskets scored and y = the number of 3 point baskets scored, that gives us an equation of 2x + 3y = 1000. 

 

We also know that there were a total of 440 2 or 3 point baskets scored. Using x and y as defined before, we get an equation of x + y = 440. 

 

To solve this, we can use substitution. Let's solve for x in terms of y for the second equation.

 

So x + y = 440. If we subtract y from both sides, we get x = 440 - y. Now we substitute 440 - y for x in the first equation. 

 

2*(440-y) + 3y = 1000. Now we simply solve the equation.

880 - 2y + 3y = 1000.

880 + y = 1000.

y = 120. 

 

So 120 of the baskets scored were 3 point baskets. 

 

If we want to solve for x, we can substitute in the known value of y to the first equation 

x + 120 = 440.

x = 320. 

 

So 320 of the baskets scored were 2 point baskets.