10% of Tim's savings was $16 more than 40% of Billy's savings. After Tim spent ¹₄ of his savings and Billy spent 40% of his savings, Billy had $264 less than Tim. How much was Billy's saving at first?

	Billy	Tim
Before	5 u	20 u + 160
Change	- 2 u	- 5 u - 40
After	3 u	15 u + 120
Comparing Billy and Tim in the end		264 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Tim = ²₅ Billy + 16 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Tim = 2x15x1 Billy + 16 
220 Tim = 25 Billy + 16 

Simplify the fractions.
¹₂₀ Tim = ¹₅ Billy + 8

Let ¹₅ Billy be 1 u.

Billy's savings at first = 5 u

¹₂₀ Tim = ¹₅ Billy + 8
Let ¹₂₀ Tim be 1 u + 8.

Tim's savings at first
= 20 x (1 u + 8) 
= 20 u + 160

Savings that Billy spent
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u
= 2 u

Savings that Tim spent 
= ¹₄ x (20 u + 160)
= 5 u + 40 

Billy had $264 less than Tim in the end. If another $264 was given to Billy, the amount that each had in the end would be the same.

15 u + 120 = 3 u + 264 
15 u - 3 u = 264 - 120
12 u = 144

1 u = 144 ÷ 12 = 12

Savings that Billy had at first
= 5 u 
= 5 x 12
= $60

Answer(s): $60