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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?

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Answer:

Total amount Silas and Raja has at first = $252

Step-by-step explanation:

Let,

Amount Silas had = x

Amount Raja had = y

According to given statement;

x = 3y       Eqn 1

x-84 = y+42     Eqn 2

Putting value of x from Eqn 1 in Eqn 2

3y - 84 = y+42

3y-y = 42+84

2y = 126

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{126}{2}\\y=63[/tex]

Putting y = 63 in Eqn 1

x = 63(3)

x = 189

Total amount they had = 189 + 63 = $252

Hence,

Total amount Silas and Raja has at first = $252

The amount they have altogether at first is $252

Let

Raja money = x

Silas had 3 times as much money as Raja. Therefore, Silas money is as follows:

  • 3x

Silas spent $84 of his money to buy a birthday gift for his grandma. Therefore, he has the following amount:

  • 3x - 84

Raja was awarded $42 for winning a competition. Therefore, Raja amount is as follows;

  • x + 42

In the end, they had the same amount of money. Therefore,

  • 3x - 84 = x + 42

3x - 84 = x + 42

3x - x = 42 + 84

2x = 126

x = 126 / 2

x = 63

Total amount(at first):

  • x + 3x = 63 + 3(63) = $252

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