what would be the equation for this math problem so i can figure it out
In a basketball game, the Squirrels scored a total of 103 points and made 3 times as many field goals ( 2 points each) as free throws (1 point each). They also made eleven three point baskets. How many field goals did they have?
let the number of free throws be T
let the number of field goals b G
G = 3T
2G + T = 130
sub the first equation into the second and solve for G
sub that back into the first
11 * 3 = 33 points from outside so that leaves 103-33 = 70 points
x = number of field goals
x/3 = number of free throws
so
70 points = 2 x + 1 (x/3)
210 = 6 x + x
7 x = 210
x = 30
oops,
I always told my students, the first step is to read the question carefully at least 2 times
and guess what, I did not read the question carefully enough, and forgot about the 3 pointers.
Either change my second equation to
2G + T = 103 - 9
or follow Damon's solution below
ARGGGG!!!!
2G + T = 103 - 9
should say
2G + T = 103 - 33
To solve this problem, we can use algebraic equations. Let's define some variables:
Let's call the number of field goals made as 'F',
the number of free throws made as 'T',
and the number of three-point baskets made as 'B'.
We know that the Squirrels made 3 times as many field goals as free throws, so we can write the equation:
F = 3T
We also know that each field goal is worth 2 points, each free throw is worth 1 point, and there were a total of 103 points. So we can express that as an equation:
2F + 1T + 3B = 103
Lastly, we are given that they made eleven three-point baskets, so we can write the equation:
B = 11
Now we have a system of three equations with three unknowns. We can substitute the value of 'B' into the other two equations, solve for 'F' and 'T', and find the number of field goals.
I hope that helps you set up the equations and solve the problem! Let me know if you have any further questions.