MATH SOLVE

4 months ago

Q:
# 17. A bag contains 10 white golf balls and 6 striped golf balls. A golfer wants to add 112 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?

Accepted Solution

A:

Originally, there are 10 white golf balls and 6 striped golf balls.

The ratio of white to striped balls is

10/6 = 5/3

Let 112 more balls be added, so that

w = white balls are added

s = striped balls are added.

Then w + s = 112 (1)

To preserve the ratio of white to striped balls,

(10 + w)/(6 +s) = 5/3.

That is (by cross multiplying),

3(10 + w) = 5(6 + s) (2)

30 + 3w = 30 + 5s

3w = 5s

w = (5/3)s (3)

Substitute (3) into (1).

(5/3)s + s = 112

(8/3)s = 112

s = (3/8)*112 = 42

w = (5/3)*42 = 70

Answer

70 white balls added

42 striped balls added

The ratio of white to striped balls is

10/6 = 5/3

Let 112 more balls be added, so that

w = white balls are added

s = striped balls are added.

Then w + s = 112 (1)

To preserve the ratio of white to striped balls,

(10 + w)/(6 +s) = 5/3.

That is (by cross multiplying),

3(10 + w) = 5(6 + s) (2)

30 + 3w = 30 + 5s

3w = 5s

w = (5/3)s (3)

Substitute (3) into (1).

(5/3)s + s = 112

(8/3)s = 112

s = (3/8)*112 = 42

w = (5/3)*42 = 70

Answer

70 white balls added

42 striped balls added