SOLUTION: Sandy Brondello scored 24 points in a recent basketball game without making any 3-point shots. She scored 16 times, making several free throws worth 1 point each and several field

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Question 1196561: Sandy Brondello scored 24 points in a recent basketball game without making any 3-point
shots. She scored 16 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?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This was already asked and answered a few minutes ago.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

Just solved under this link

https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.1196558.html

https://www.algebra.com/algebra/homework/word/mixtures/Mixture_Word_Problems.faq.question.1196558.html



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor shows a good typical formal algebraic solution -- which is probably what you were looking for.

However, you can get good mental problem-solving practice by solving the problem informally, using logical reasoning and simple arithmetic. Here are a couple of different ways.

(1) 16 1-point free throws would have scored only 16 points; the actual total was 24-16 = 8 more than that. Since each field goal is worth 1 point more than each free throw, the number of field goals must have been 8.

(2) 24 points on 16 shots is an average of 24/16 = 1.5. Since the average is exactly halfway between 1 and 2, the numbers of free throws and field goals must have been the same, so the number of field goals was 16/2 = 8.