Split costs and one pay $X%$ more?

Question

If combined costs are 23000 and you where to split it in two 
and then one should pay 18% more, how do you count that?

23 000 / 2 = 11 500
11 500 * 0.82 = 9 430
11 500 - 9 430 = 2 070
11 500 + 2 070 = 13 570

so its 13 570 for one to pay and 9 430 for the other? , isnt that 30% more?

( (13 570-9 430) / 13 570) = 0.31 = 31% ?

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Is this calc wrong?

218 = 100 + 100 + X% (X = 18)

23 000 / 218 = 105.5

105.5 * 100 = 10 550
105.5 * 118 = 12 449.5

so one pay 10 550 and the other 12 449.5?

Answer 1

Let me see if I understand the question. See below...

We have $23,000. It must be split among two individual such that one person pays 18% more than the other person. What does each person pay?

Let $x$ represent the smaller amount that one individual pays. Then the other individual, who pays $18\%$ more must pay $x+0.18x = 1.18x$.

Together, they must have $23,000, so

$$x + 1.18x = 23000$$ $$2.18x = 23000$$ $$x \approx \$10550.46$$

That's the amount one pays. The other pays

$$1.18x \approx \$12449.54$$