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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Answers
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
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
Initially they have $252 altogether if Silas had 3 times as much money as Raja. Silas spent $84 and Raja was awarded $42 and in the end they had the same amount of money
Given:
- Silas had 3 times as much money as Raja
- Silas spent $84 of his money to buy a birthday gift for his grandma
- Raja was awarded $42 for winning a competition
- In the end, they had the same amount of money.
To Find:
- Amount they have altogether at first
Solution:
Step 1:
Assume that Initially Raja had x$ and Silas had 3x $ Hence,
Altogether initially = x + 3x = $ 4x
Step 2:
Silas spent $84 Hence amount left with Silas
$ 3x - 84
Step 3:
Raja Awarded $42 Hence amount with Raja
$ x + 42
Step 4:
Equate both the amount and solve for x
3x - 84 = x + 42
=> 2x = 126
=> x = 63
Step 5:
Substitute x = 63 and calculate 4x
4x = 4(63)
=> 4x = 252
Hence , Initially they have $252 altogether