Kimberly and Mike have an equal amount of money. After Kimberly spent $50 and Mike spent $25, Mike's money is 50% more than Kimberly's. How much did Kimberly and Mike have at first?

Kimberly and Mike had at first $100 each

Step-by-step explanation:

Assume that Kimberly and Mike each have $x

∵ Kimberly has $x

∵ Kimberly spent $50

- Find the reminder with Kimberly by subtracting 50 from x

∴ The money left with Kimberly = x - 50

∵ Mike has $x

∵ Mike spent $25

- Find the reminder with Mike by subtracting 25 from x

∴ The money left with Mike = x - 25

∵ Mike's money is 50% more than Kimberly's money

- That means Mike's money is more than Kimberly's money by

   50% of Kimberly's money

∴ x - 25 = (x - 50) + 50%(x - 50)

∵ 50% = = 0.5

∴ x - 25 = (x - 50) + 0.5(x - 50)

- Simplify the right hand side

∴ x - 25 = x - 50 + 0.5x - 25

- Add the like terms in the right hand side

∴ x - 25 = 1.5x - 75

- Add 75 to both sides

∴ x + 50 = 1.5x

- Subtract x from both sides

∴ 50 = 0.5x

- Divide both sides by 0.5

∴ 100 = x

∵ x represents the amount of money that Kimberly and

   Mike each had at first

∴ Kimberly and Mike had at first $100 each

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.