Jennifer had 3 times as much coffee powder as Mie at first. After Jennifer gave 16.77 kg of coffee powder to Mie, Jennifer had 77.5 kg more coffee powder than Mie. How much coffee powder did Mie have at first?
J = Jennifer's coffee powder at first
M = Mie's coffee powder at first
Jennifer had 3 times as much coffee powder as Mie at first, means:
J = 3 M
After Jennifer gives 16.77 kg to Mie Jennifer has J - 16.77 kg of coffee powder.
Mie has M + 16.77 kg of coffee powder.
Now Jennifer had 77.5 kg more coffee powder than Mie, this means:
J - 16.77 = M + 16.77 + 77.5
J - 16.77 = M + 94.27
Add 16.77 to both sides
J = M + 111.04
Replace J by 3M in this equation.
3 M = M + 111.04
Subtract M to both sides.
2 M = 111.04
M = 111.04 / 2
M = 55.52
At first Mie have 55.52 kg coffee powder.
Check result.
At first Jennifer have 3 M = 3 ∙ 55.52 = 166.56 kg coffee powder
After Jennifer gives 16.77 kg to Mie Jennifer has 166.56 - 16.77 = 149.79 kg of coffee powder.
Mie has 55.52 + 16.77 = 72.29 kg of coffee powder.
Jennifer's coffee powder - Mie's coffee powder = 149.79 - 72.29 = 77.5 kg
Jennifer had 77.5 kg more coffee powder than Mie.
Let's assume that Mie had x kg of coffee powder at first.
Jennifer had 3 times as much coffee powder as Mie, so Jennifer had 3x kg of coffee powder at first.
After Jennifer gave 16.77 kg of coffee powder to Mie, Jennifer had 3x - 16.77 kg of coffee powder.
Jennifer had 77.5 kg more coffee powder than Mie, so we can set up the following equation:
3x - 16.77 = x + 77.5
Simplifying the equation, we have:
2x = 94.27
Dividing both sides of the equation by 2, we find:
x = 47.135
Therefore, Mie had approximately 47.135 kg of coffee powder at first.