30% of Harry's savings was $114 more than 40% of Sam's savings. After Harry spent ³₁₀ of his savings and Sam spent 40% of his savings, Harry had $296 more than Sam. How much was Harry's saving at first?

	Sam	Harry
Before	15 u	20 u + 380
Change	- 6 u	- 6 u - 114
After	9 u	14 u + 266
Comparing Sam and Harry in the end		296 more

30% = ³⁰₁₀₀ = ³₁₀

40% = ⁴⁰₁₀₀ = ²₅

³₁₀ Harry = ²₅ Sam + 114 

Make the numerators the same. LCM of 3 and 2 is 6.
 
3x210x2 Harry = 2x35x3 Sam + 114 
620 Harry = 615 Sam + 114 

Simplify the fractions.
¹₂₀ Harry = ¹₁₅ Sam + 19

Let ¹₁₅ Sam be 1 u.

Sam's savings at first = 15 u

¹₂₀ Harry = ¹₁₅ Sam + 19
Let ¹₂₀ Harry be 1 u + 19.

Harry's savings at first
= 20 x (1 u + 19) 
= 20 u + 380

Savings that Sam spent
= 40% x 15 u
= ⁴⁰₁₀₀ x 15 u
= 6 u

Savings that Harry spent 
= ³₁₀ x (20 u + 380)
= 6 u + 114 

Harry had $296 more than Sam in the end. If another $296 was given to Sam, the amount that each had in the end would be the same.

14 u + 266 = 9 u + 296 
14 u - 9 u = 296 - 266
5 u = 30

1 u = 30 ÷ 5 = 6

Savings that Harry had at first
= 20 u + 380
= 20 x 6 + 380
= 120 + 380
= $500

Answer(s): $500