Answer:70 white golf balls and 42 striped golf balls
Step-by-step explanation:
First we find the ratio of white to striped balls
White golf balls = 10
Striped golf balls = 6
Ratio = 10/6 = 5/3
We are told a golfer wants to add extra 112 balls to the already 16 balls
And the ratio after adding 112 balls must stay the same
First we label the extra golf balls to be added x and y
x = white golf balls
y = striped golf balls
So since we know the 112 balls added is a combination of the extra white golf balls and striped golf balls, we create an equation for that, labelling it (1)
x + y = 112 (1)
And we are told that after putting these extra balls the ratio must remain the same, which is 5/3
which will be (10 white balls + x) divided by (6 striped ball + y) will be equals to 5/3
So we create another equation for this, labelling it (2)
(10+x)/(6+y) = 5/3 (2)
So we have two simultaneous equations
We pick (1)
x + y = 112
We either make x or y the subject of formula, I choose to make x the subject of formula, we label the equation (3)
take y to the other side, causing it to change to -y
x = 112 - y (3)
We then work with (2)
(10+x)/(6+y) = 5/3
We cross multiply
3(10+x) = 5(6+y)
We open the brackets
Making the equation simplified and labelling it (4)
30 +3x = 30 + 5y
Collect like terms
3x -5y = 30-30
3x -5y = 0 (4)
Remember from (3) we know that
x = 112 -y
So we put (3) in (4)
3(112 - y) - 5y = 0
Open bracket
336 -3y -5y =0
336 -8y = 0
Transfer -8y to the other side, changing to +8y
336 = 8y
Divide both sides by 8
336/8 = y
42 = y
y = 42
from (3) we know that x equals 112 - y
So we put y = 42 in (3)
x = 112 - y
x = 112 -42 = 70
x = 70
So therefore number of white golfs balls and striped golfs balls to be added to keep the same ratio is 70 and 42 respectively
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