A bag contains 16 white golf balls and 8 striped golf balls. A golfer wants to add 132 golf balls to the bag. He wants the ratio of white to striped golf balls to remain the same. How many of each should he add?
This is not a test question i just suck at these
present ratio of white :striped = 16:8 = 2:1
white added = x
striped added = 132-x
(16 + x)/(8 + 132-x) = 2/1
16+x = 16 + 264 - 2x
3x = 264
x = 88
he should add 8 whites and 44 whites
check:
new whites = 16+88 = 104
new stripes = 8+44 = 52
104:52 = 2:1
To solve this problem, we need to find the ratio of white to striped golf balls in the original bag and maintain the same ratio after adding 132 golf balls.
Step 1: Determine the ratio of white to striped golf balls in the original bag.
In the original bag, there are 16 white golf balls and 8 striped golf balls. The ratio of white to striped golf balls can be expressed as 16:8. Simplifying this ratio gives us 2:1.
Step 2: Determine the number of white golf balls to be added.
Since the original ratio is 2:1, for every 2 white golf balls, there is 1 striped golf ball. To maintain this ratio, we need to add golf balls in the same proportion. Therefore, for every 2 white golf balls added, we need to add 1 striped golf ball.
Step 3: Calculate the number of sets of 2 white golf balls.
To find the number of sets of 2 white golf balls, we divide the total number of white golf balls to be added (unknown) by 2. So, the number of sets of 2 white golf balls is x/2.
Step 4: Calculate the number of striped golf balls to be added.
Since for every 2 white golf balls added, we need to add 1 striped golf ball, the number of striped golf balls to be added will be half of the number of sets of 2 white golf balls added. So, the number of striped golf balls to be added is (x/2) / 2 = x/4.
Now, we can set up an equation to represent the given information:
(x/4) / (x/2) = 8/16.
Step 5: Solve the equation for x.
By cross-multiplication, we can solve the equation:
(2x) (8) = (4) (16).
16x = 64.
Dividing both sides by 16:
x = 4.
Therefore, the golfer should add 4 sets of 2 white golf balls (8 white golf balls) and 1 set of 1 striped golf ball to maintain the ratio of white to striped golf balls.
No problem! Let's work through it together step by step.
Step 1: Determine the current ratio of white to striped golf balls in the bag.
Currently, there are 16 white golf balls and 8 striped golf balls. So the ratio is 16:8, which simplifies to 2:1.
Step 2: Set up a ratio equation using the current ratio.
Let's assume the golfer adds 'x' number of white golf balls and 'y' number of striped golf balls. The ratio of white to striped golf balls after adding the new balls should still be 2:1.
So, the equation will be: (16 + x):(8 + y) = 2:1
Step 3: Solve the ratio equation.
To find the values of 'x' and 'y', we need to solve the equation.
(16 + x) / (8 + y) = 2 / 1
Cross-multiplying gives us:
2(8 + y) = 1(16 + x)
Simplifying and removing the parentheses:
16 + 2y = 16 + x
Subtracting 16 from both sides:
2y = x
We now have a relationship between 'x' and 'y' - "2y = x".
Step 4: Determine the number of each ball to be added.
Since we are given that the golfer wants to add 132 golf balls, we need to find the values of 'x' and 'y' that satisfy the equation while maintaining the desired ratio.
To solve, we can substitute the value of 'x' from the relationship obtained in Step 3 into the equation:
2y = x
Substituting 'x' with '2y':
2y = 2y
This shows that 'x' and 'y' can have any value as long as they are equal to each other.
Step 5: Determine the values of 'x' and 'y' based on the given conditions.
Since the golfer wants to add a total of 132 golf balls, the values of 'x' and 'y' need to be equal and sum up to 132.
One possible solution could be:
x = 66
y = 66
Thus, the golfer should add 66 white golf balls and 66 striped golf balls to maintain the desired ratio of 2:1.