Question

In a basketball game, a regular basket is worth 2 points and a long distance basket is worth 3 points. There were 54 baskets in a game and 118 points total. Part A: Write a system of equations where x represents a regular basket and y represents a long distance basket.

Answer 1

The system of equations for the given situation is:

`x+y=54`

`2x+3y=118`

Explanation:

Given:

Regular basket is worth = 2 points

Long distance basket is worth =3 points

Total baskets in a game = 54

Total points in total = 118

`x\rightarrow` represents the number of regular baskets

`y\rightarrow` represents the number of long distance baskets.

Expression for total baskets can be given by ⇒
`x+y`

Thus first equation representing total baskets in a game is given by:

`x+y=54`

Since a regular basket is worth 2 points

So
`x` regular baskets would be worth
`=2x` points

Since a long distance basket is worth 3 points

So
`y` long distance baskets would be worth
`=3y` points

Expression for total points in a game can be given by ⇒
`2x+3y`

Thus second equation representing total points in a game is given by:

`2x+3y=118`

∴ The system of equations for the given situation is:

`x+y=54`

`2x+3y=118`