Two bags had 50 kilograms of sugar each. After taking out 3 times as much sugar from bag one than bag two, bag one had half as much sugar left as bag two. How much sugar is left in each bag?
Answers
From question
50 - 3x = 1/2 (50-x)
Multiply both sides by 2 (to eliminate the 1/2
100-6x= 50-x
Add 6x to both sides
100= 50-5x
Subtract 50 from both sides
50=5x
Lastly, divide by 5
10=x
So, 10 kg of sugar was removed from bag 2.
3x= 30, so 30 kg of sugar was removed from bag 1.
50-30=20 kg remaining in bag 1.
50-10=40 kg remaining in bag 2.
Weight of 1 bag = 50kg
Define x:
Let the amount taken out from bag two be x
Amount taken out from bag one = 3x
Form equation:
bag one had 1/2 as much left as bag 2
⇒ 50 - 3x = 1/2 (50 - x)
Solve x:
50 - 3x = 1/2 (50 - x)
Multiply by 2 on both sides:
100 - 6x = 50 - x
Add x to both sides:
100 - 5x = 50
Subtract 100 on both sides:
-5x = -50
Divide both sides by -5:
x = 10
Find the amount of sugar left:
Bag one = 50 - 3x = 50 - 3(10) = 20 kg
Bag two = 50 - x = 50 - 10 = 40 kg
Answer: Bag one has 20 kg left and bag two has 40 kg left.