Mrs Ma had a sum of money. She gave her son $630 and gave ¹₄ of the remaining money to her mother. She used ⁴₅ of the rest of the money on a home theater system and was left with ¹₁₀ of the amount she had at first. What was the sum of money she had at first?

Her son	Her mother	Remaining amount		Total
$630	1x5	3x5
		Home Theater System	Left
		4x3	1x3
9x3 = 27 u			1x3 = 3 u
10 u	5 u	12 u	3 u	30 u

Fraction of the remaining amount left 
= 1 - ⁴₅
= ¹₅

The remaining amount is repeated.  Make the remaining amount the same. LCM of 3 and 5 is 15. 

The amount left is repeated.  Make the amount left the same.

¹₅ Remaining amount = ¹₁₀ Total amount

Amount that Mrs Ma gave to her son
= 27 u - 5 u - 12 u
= 10 u

10 u = 630

1 u = 630 ÷ 10 = 63

Total amount that Mrs Ma had at first
= 10 u + 5 u + 12 u + 3 u
= 30 u
= 30 x 63
= $1890

Answer(s): $1890