10% of Charlie's savings was $51 more than 30% of Jeremy's savings. After Charlie spent ³₅ of his savings and Jeremy spent 40% of his savings, Charlie had $258 more than Jeremy. How much was Charlie's saving at first?

	Jeremy	Charlie
Before	10 u	30 u + 510
Change	- 4 u	- 18 u - 306
After	6 u	12 u + 204
Comparing Jeremy and Charlie in the end		258 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Charlie = ³₁₀ Jeremy + 51 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Charlie = 3x110x1 Jeremy + 51 
330 Charlie = 310 Jeremy + 51 

Simplify the fractions.
¹₃₀ Charlie = ¹₁₀ Jeremy + 17

Let ¹₁₀ Jeremy be 1 u.

Jeremy's savings at first = 10 u

¹₃₀ Charlie = ¹₁₀ Jeremy + 17
Let ¹₃₀ Charlie be 1 u + 17.

Charlie's savings at first
= 30 x (1 u + 17) 
= 30 u + 510

Savings that Jeremy spent
= 40% x 10 u
= ⁴⁰₁₀₀ x 10 u
= 4 u

Savings that Charlie spent 
= ³₅ x (30 u + 510)
= 18 u + 306 

Charlie had $258 more than Jeremy in the end. If another $258 was given to Jeremy, the amount that each had in the end would be the same.

12 u + 204 = 6 u + 258 
12 u - 6 u = 258 - 204
6 u = 54

1 u = 54 ÷ 6 = 9

Savings that Charlie had at first
= 30 u + 510
= 30 x 9 + 510
= 270 + 510
= $780

Answer(s): $780