MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

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:

[tex] \left \{ {{x+y=23} \atop {2x+3y=53}} \right. [/tex]

Isolate for [tex]x[/tex] in Equation #1:

[tex]x+y=23[/tex]

[tex]x=23-y[/tex]

Substitute the new Equation #1 into Equation #2:

[tex]2x+3y=53[/tex]

[tex]2(23-y)+3y=53[/tex]

Solve for [tex]y[/tex] :

[tex]2(23-y)+3y=53[/tex]

Distribute the Parenthesis:

[tex]46-2y+3y=53[/tex]

Combine like terms:

[tex]46+y=53[/tex]

Add -46 to both sides:

[tex](46+y)+(-46)=(53)+(-46)[/tex]

[tex]y=7[/tex]

Substitute this value into Equation #1:

[tex]x+y=23[/tex]

[tex]x+(7)=23[/tex]

Add -7 to both sides:

[tex](x+7)+(-7)=(23)+(-7)[/tex]

[tex]x=16[/tex]

The Solution Is:

[tex]\boxed{(16,7)}[/tex]

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

I hope this helped!

-Benjamin

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:

[tex] \left \{ {{x+y=23} \atop {2x+3y=53}} \right. [/tex]

Isolate for [tex]x[/tex] in Equation #1:

[tex]x+y=23[/tex]

[tex]x=23-y[/tex]

Substitute the new Equation #1 into Equation #2:

[tex]2x+3y=53[/tex]

[tex]2(23-y)+3y=53[/tex]

Solve for [tex]y[/tex] :

[tex]2(23-y)+3y=53[/tex]

Distribute the Parenthesis:

[tex]46-2y+3y=53[/tex]

Combine like terms:

[tex]46+y=53[/tex]

Add -46 to both sides:

[tex](46+y)+(-46)=(53)+(-46)[/tex]

[tex]y=7[/tex]

Substitute this value into Equation #1:

[tex]x+y=23[/tex]

[tex]x+(7)=23[/tex]

Add -7 to both sides:

[tex](x+7)+(-7)=(23)+(-7)[/tex]

[tex]x=16[/tex]

The Solution Is:

[tex]\boxed{(16,7)}[/tex]

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

I hope this helped!

-Benjamin