10% of Dylan's savings was $51 more than 30% of Fred's savings. After Dylan spent ²₃ of his savings and Fred spent 40% of his savings, Fred had $246 less than Dylan. How much was Fred's saving at first?

	Fred	Dylan
Before	10 u	30 u + 510
Change	- 4 u	- 20 u - 340
After	6 u	10 u + 170
Comparing Fred and Dylan in the end		246 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Dylan = ³₁₀ Fred + 51 

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

Simplify the fractions.
¹₃₀ Dylan = ¹₁₀ Fred + 17

Let ¹₁₀ Fred be 1 u.

Fred's savings at first = 10 u

¹₃₀ Dylan = ¹₁₀ Fred + 17
Let ¹₃₀ Dylan be 1 u + 17.

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

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

Savings that Dylan spent 
= ²₃ x (30 u + 510)
= 20 u + 340 

Fred had $246 less than Dylan in the end. If another $246 was given to Fred, the amount that each had in the end would be the same.

10 u + 170 = 6 u + 246 
10 u - 6 u = 246 - 170
4 u = 76

1 u = 76 ÷ 4 = 19

Savings that Fred had at first
= 10 u 
= 10 x 19
= $190

Answer(s): $190