A bag contains a total of 16 golf balls, 6 of which are white a golfer bolts, to add a 112 golf balls to the bag. He wants the ratio of white to striped golf balls to remain the same. How many of eat should he add

Question

A bag contains a total of 16 golf balls, 6 of which are white a golfer bolts, to add a 112 golf balls to the bag. He wants the ratio of white to striped golf balls to remain the same. How many of eat should he add

Answer 1

To solve this problem, we have to maintain the same ratio of white to striped golf balls after adding 112 golf balls to the bag. Currently, there are 6 white golf balls in the bag out of 16 total golf balls, so the rest must be striped.

Let's first calculate how many striped golf balls there are:
Total golf balls in the bag = 16
White golf balls in the bag = 6

Striped golf balls in the bag = Total golf balls - White golf balls
Striped golf balls in the bag = 16 - 6 = 10

Now we have 6 white and 10 striped golf balls, which gives us a ratio of white to striped golf balls of 6:10. We can simplify this ratio by dividing both numbers by their greatest common divisor, which is 2:

6 ÷ 2 = 3
10 ÷ 2 = 5

So the simplified ratio of white to striped golf balls is 3:5.

The golfer wants to add 112 golf balls while maintaining this ratio. Let's use "w" for the number of white balls to be added and "s" for the number of striped balls to be added. The ratio of w to s should be the same as the ratio of white to striped golf balls we currently have, which is 3:5:

w/s = 3/5

We know that the total number of additional golf balls w + s should be equal to 112, so we can write a second equation:

w + s = 112

We can use these two equations together to solve for w and s. From the ratio equation, we know:

w = (3/5) * s

And from the total equation, substituting w we get:

(3/5) * s + s = 112

Combine like terms (common denominator is 5):

(3s + 5s) / 5 = 112

Multiply both sides by 5 to eliminate the fraction:

8s = 112 * 5

Now solve for s:

s = (112 * 5) / 8
s = 560 / 8
s = 70

Now that we have s, the number of striped balls to be added, we can find w using the total equation:

w + s = 112
w + 70 = 112
w = 112 - 70
w = 42

Therefore, the golfer should add 42 white golf balls and 70 striped golf balls to maintain the same ratio of white to striped golf balls in the bag.