Question

Tina Thompson scored 34 points in a recent basketball game without making any 3- point shots. She scored 23 times, making several free throws worth 1 point each and several field goals worth two points each. How many free throws did she make? How many 2 point field goals did she make?

Answer 1

Explain in terms that someone who does not know what they are doing can figure this out. Step by step.

Answer 2

X+Y=23
X=23-Y REPLACE X BY (23-Y) IN THE NEXT EQUATION & SOLVE FOR Y.
1X+2Y=36
(23-Y)+2Y=36
23+Y=36
Y=36-23


Y=13 2 POINT SHOTS WERE MADE.
X+13=23
X=23-13
X=10 FREE THROWS WERE MADE.
PROOF:
1*10+2*13=36
10+26=36
36=36

Answer 3

well its simultaneous equations

let x = field goals....and y = free throws

shots
x + y = 23

scoring

2x + 1y = 34


so the easiest is to use substitution...

take the 1st equation and make y the subject

y = 23 - x

and substitute it into the scoring

2x +(23 - x) = 34

now solve for x

this will be the number of 2 point shots...

substitute the value into the 1st equation to find the number of free throws.

Answer 4

I don't understand how that means substitute into the scoring. .where did y go?

Answer 5

can you see how I took the shoting equation

x + y = 23

and made y the subject

y = 23 - x...?

Answer 6

yes

Answer 7

What happens after 2x+(23-x)=34?

Answer 8

well it becomes

2x + 23 - x = 34

does that make sense..?

Answer 9

right so x+23=34 subtract 23 from both sides making it 11 right?

Answer 10

so 11 field goals

Answer 11

thats correct... 11 from the field = 22 points...

so if there were 23 shots ... how many free throws...?

Answer 12

12

Answer 13

thats it... well done