Question

in the basketball game Jake made 23 baskets each of the baskets was worth either two or three points and Jake scored a total of 53 points how many two-point and three-point baskets did Jake make

Answer 1

(16,7) is the answer

Answer 2

Greetings!

Let x represent the number of 2 pointers made.
Let y represent the number of 3 pointers made.

We have to create a system of equations to solve this problem:

`\left \{ {{x+y=23} \atop {2x+3y=53}} \right.`

Isolate for
`x` in Equation #1:

`x+y=23`


`x=23-y`

Substitute the new Equation #1 into Equation #2:

`2x+3y=53`


`2(23-y)+3y=53`

Solve for
`y` :

`2(23-y)+3y=53`

Distribute the Parenthesis:

`46-2y+3y=53`

Combine like terms:

`46+y=53`

Add -46 to both sides:

`(46+y)+(-46)=(53)+(-46)`


`y=7`

Substitute this value into Equation #1:

`x+y=23`


`x+(7)=23`

Add -7 to both sides:

`(x+7)+(-7)=(23)+(-7)`


`x=16`

The Solution Is:

`\boxed{(16,7)}`

Jake made 16 two-pointers and 7 three-pointers!

I hope this helped!
-Benjamin