a bag contains 10 white gold 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

Answer:70 white golf balls and 42 striped golf ballsStep-by-step explanation:First we find the ratio of white to striped ballsWhite golf balls = 10Striped golf balls = 6Ratio = 10/6 = 5/3We are told a golfer wants to add extra 112 balls to the already 16 ballsAnd the ratio after adding 112 balls must stay the sameFirst we label the extra golf balls to be added x and yx = white golf ballsy = striped golf ballsSo 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 5/3which will be (10 white balls + x) divided by (6 striped ball + y) will be equals to 5/3So we create another equation for this, labelling it (2)(10+x)/(6+y) = 5/3 (2)So we have two simultaneous equationsWe pick (1)x + y = 112We 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 -yx = 112 - y (3)We then work with (2)(10+x)/(6+y) = 5/3We cross multiply 3(10+x) = 5(6+y)We open the bracketsMaking the equation simplified and labelling it (4)30 +3x = 30 + 5yCollect like terms3x -5y = 30-30 3x -5y = 0 (4)Remember from (3) we know that x = 112 -ySo we put (3) in (4)3(112 - y) - 5y = 0Open bracket 336 -3y -5y =0336 -8y = 0Transfer -8y to the other side, changing to +8y336 = 8yDivide both sides by 8336/8 = y42 = yy = 42from (3) we know that x equals 112 - ySo we put y = 42 in (3)x = 112 - yx = 112 -42 = 70x = 70So therefore number of white golfs balls and striped golfs balls to be added to keep the same ratio is 70 and 42 respectively