Over a period of 5 games a basketball team made exactly 44% of their shots. the number of shots taken was more than 310 and less than 350. How many shots were made?
let x be the total number of shots taken
then ( 44/100)x must be an integer
(11/25)x must be an integer
the number must end in 25 or 00 to be divisible by 25
so within your domain given, the number must be 325
They must have taken 325 shots
check:
44% of 325 = .44(325) = 143
and 143/325 = .44 = 44%
To find the number of shots made, we need to determine the total number of shots taken.
1. Let's assume that the number of shots taken is x.
2. We know that the team made exactly 44% of their shots, which means they made (44/100) * x shots.
3. We can set up an equation to solve for x: (44/100) * x = shots made.
4. To narrow down the possible values of x, we use the given information that the number of shots taken is more than 310 and less than 350.
So, we have the inequality: 310 < x < 350.
Now, we can solve the equation and find the number of shots made.
1. Solve the equation: (44/100) * x = shots made.
Multiply both sides by 100 to remove the fraction: 44x = 100 * shots made.
Divide both sides by 44 to isolate x: x = (100 * shots made) / 44.
2. Determine the range of x: 310 < x < 350.
Substitute the equation x = (100 * shots made) / 44 into the inequality:
310 < (100 * shots made / 44) < 350.
3. Simplify the inequality:
Multiply all parts of the inequality by 44 to get rid of the fraction: 310 * 44 < 100 * shots made < 350 * 44.
Simplify: 13,640 < 100 * shots made < 15,400.
Now, we need to find the value of shots made that satisfies this inequality.
4. Divide all parts of the inequality by 100: 136.4 < shots made < 154.
Since the number of shots made has to be a whole number, we can conclude that the team made 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, or 153 shots.
Therefore, the team made between 137 and 153 shots.