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]