30% of Ben's savings was $78 more than 40% of Tommy's savings. After Ben spent ¹₄ of his savings and Tommy spent 40% of his savings, Tommy had $279 less than Ben. How much was Tommy's saving at first?

	Tommy	Ben
Before	15 u	20 u + 260
Change	- 6 u	- 5 u - 65
After	9 u	15 u + 195
Comparing Tommy and Ben in the end		279 more

30% = ³⁰₁₀₀ = ³₁₀

40% = ⁴⁰₁₀₀ = ²₅

³₁₀ Ben = ²₅ Tommy + 78 

Make the numerators the same. LCM of 3 and 2 is 6.
 
3x210x2 Ben = 2x35x3 Tommy + 78 
620 Ben = 615 Tommy + 78 

Simplify the fractions.
¹₂₀ Ben = ¹₁₅ Tommy + 13

Let ¹₁₅ Tommy be 1 u.

Tommy's savings at first = 15 u

¹₂₀ Ben = ¹₁₅ Tommy + 13
Let ¹₂₀ Ben be 1 u + 13.

Ben's savings at first
= 20 x (1 u + 13) 
= 20 u + 260

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

Savings that Ben spent 
= ¹₄ x (20 u + 260)
= 5 u + 65 

Tommy had $279 less than Ben in the end. If another $279 was given to Tommy, the amount that each had in the end would be the same.

15 u + 195 = 9 u + 279 
15 u - 9 u = 279 - 195
6 u = 84

1 u = 84 ÷ 6 = 14

Savings that Tommy had at first
= 15 u 
= 15 x 14
= $210

Answer(s): $210