Question

Leonora made 141414 total baskets during her basketball game. During the game, she made xxx baskets worth 222 points each and yyy baskets worth 333 points each. If she scored 303030 points total throughout the game, how many 222-point baskets did she make

1. niczorrrr
Leonora made 12 number of 2-point baskets, solved using the system of equations
We are asked that if she scored 30 points total throughout the game, how many 2-points basket did she make.
Number of 2-points basket scored = x.
Number of 3-points basket scored = y.
Thus, total number of baskets scored = x + y.
But, the total number of baskets scored is given to be 14.
Thus, we get an equation x + y = 14 … (i).
The total worth of 2-points basket scored = 2x.
The total worth of 3-points basket scored = 3y.
Thus, the total points scored = 2x + 3y.
But, the total points scored is given to be 30.
Thus, we get an equation 2x + 3y = 30 … (ii).
(i) and (ii) together gives us a system of equation.
To solve the system of equations, we multiply (i) by 3, and then subtract (ii) from it.
3x + 3y = 42
2x + 3y = 30.
(-) (-)     (-)
__________
x = 12.
Thus, Leonora made 12 number of 2-point baskets, solved using the system of equations.