Question 736146: A basketball player scored 18 times during one game. He scored a total of 30 points, which consists of 1 point free throws and 2 point baskets. How many one point free throws did he make? How many 2 point baskets did he make?
Found 5 solutions by lynnlo, ikleyn, Edwin McCravy, greenestamps, mccravyedwin:
Answer by lynnlo(4176)   (Show Source):
You can put this solution on YOUR website! SCORE========================18TIMES
TOTAL POINTS=============30
2 POINT SHOTS======12=(24)
1POINT FREE THROW SHOTS==6(6)
=============================
12+24====30
Answer by ikleyn(53422)  (Show Source):
You can put this solution on YOUR website! .
A basketball player scored 18 times during one game. He scored a total of 30 points, which consists
of 1 point free throws and 2 point baskets.
How many one point free throws did he make? How many 2 point baskets did he make?
~~~~~~~~~~~~~~~~~~~~~~~~~~~
There are different methods to solve this problem.
I will show here one of these methods, which is a basic.
It means that every student solving such problem/problems MUST know it.
Probably, other tutors will come and add their versions - but this one is that every student must know.
Let x be the number of 1-point throws.
Then the number of 2-point throws is (18-x).
1-point throws contribute 1*x = x points to the total counting.
2-point throws contribute 2*(18-x) points to the total counting.
Now you are prepared to write an equation for the total points
x + 2*(18-x) = 30 points total.
Simplify it and find 'x'
x + 36 - 2x = 30,
x - 2x = 30 - 36,
-x = -6,
x = 6.
Thus the number of the 1-point throws is 6.
Hence, the number of the 2-point throws is 18-6 = 12.
ANSWER. 6 one-point throws and 12 two-point throws.
Solved, and now you know the method.
Answer by Edwin McCravy(20077)  (Show Source):
Answer by greenestamps(13258)  (Show Source):
You can put this solution on YOUR website!
You have received two responses showing different ways of solving the problem. Briefly summarized, here are those two methods.
First tutor (set up the problem using only one variable)....
x = # of 1-point shot, so (18-x) = # of 2-point shots.
The point total is 30, so x(1)+2(18-x) = 30.
Solve that equation to find the answer.
Second tutor (set up the problem using two variables and two equations and solve using substitution)....
x = # of 1-point shots; y = # of 2-points shots.
The total number of shots is 18, so x+y = 18.
The point total is 30, so x(1)+2(y) = 30.
Solve the first equation for x: x = 18-y.
Substitute "18-y" for "x" in the second equation, giving x(1)+2(18-x) = 30.
At that point the equation to solve is the same as in the solution from the first tutor, so solving the problem from there is the same.
A different method for solving the problem -- which a student should also know -- is using two variables and two equations and solving the pair of equations using elimination.
x+y = 18; x+2y = 30
Subtract the first equation from the second, eliminating x: y = 12
Substitute y=12 in either equation to find x = 6
ANSWER: x = 6 1-point shots and y = 12 2-point shots
Finally, while a student should understand and be able to use either substitution or elimination to solve the problem, it should be noted that solving the problem informally, using logical reasoning and simple arithmetic instead of formal algebra, is excellent mental exercise.
For this problem, the calculations are exactly those used in the above solution using elimination. Here is how the thinking can go:
(1) If all 18 shots were 2-point shots, the point total would be 18*2 = 36.
(2) The actual point total, 30, is 6 points less than that.
(3) Since each 1-point shot is worth 1 point less than each 2-point shot, the number of 1-point shots must have been 6.
ANSWERS: 6 1-point shot; so 18-6 = 12 2-point shots
Answer by mccravyedwin(417)  (Show Source):
You can put this solution on YOUR website!
I knew in advance Greenestamps would come up with the way to solve it the same
way as the 2-legged and 4-legged animal problems, by first thinking how it would
be if they were all one or the other. Then there would either be too few or too
many legs and how many of the other type animal you would need to have to
increase or decrease the number of legs to get the given number of legs. I've
also seen bicycle/tricycle and 3 and 4-legged stool problems that could be done
the same way.
Greenestamps used the "too many points" way. I'll use the "too-few points way.
(1) If all 18 shots were 1-point free throws, (a really strange basketball
game lol), the point total would be 18*1 = 18.
(2) The actual point total, 30, is 30-18=12 more than that.
(3) So 12 of those 18 shots must be increased by 1 point to increase the
total points from 18 to 30.
ANSWERS: 12 2-point shots; so 18-12 = 6 1-point shots.
Edwin
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