Silas had 3 times as much money as Raja. Silas spent $84 of his money to buy a birthday gift for his grandma while Raja was awarded $42 for winning a competition. In the end, they had the same amount of money. How much did they have altogether at first?

Total money they had at first $252.

Step-by-step explanation:

Let,

x be the amount Silas had originally

y be the amount Raja had originally

According to given statement;

x = 3y     Eqn 1

x - 84 = y + 42    Eqn 2

Putting x=3y in Eqn 2

3y - 84 = y + 42

3y - y = 42 + 84

2y = 126

Dividing both sides by 2

Putting y = 63 in Eqn 1

x = 3(63)

x = 189

Total money they originally had = 189 + 63 = $252

Hence,

Total money they had at first $252.