# Raju had 5 times as much money as Ann. How much did Raju have at first?

• MHB
• Johnx1
In summary, Raju had 1350 dollars at first. This was found by setting up the equations R = 5A and R + A = 1560, and solving for R. After Raju gave Ann 50 dollars, Raju had 5 times as much money as Ann, leading to the equation R-50=5(A+50). Solving for R, we get the answer of 1350 dollars.
Johnx1
Raju and Ann saved a total of 1560 dollars. After Raju gave Ann 50 dollars, Raju had 5 times as much money as Ann. How much did Raju have at first?Number of dollars saved = R
Number of dollars saved = A

1) We know Raju and Ann saved 1560 dollars

R + A = 1560

2) (i got confuse at this part) Raju gave Ann 50 dollars, Raju had 5 times as much money as Ann

R = 5A (not sure if this is the correct way to do it)So then I did => 5A + A = 1560. So A = 260.

Then, I put it back to R = 5A, and then I added 50. So the answer is R = 1350.

After Raju gave Ann 50 dollars Raju had $$R-50$$ and Ann had $$A+50$$, so we want:

$$\displaystyle R-50=5(A+50)$$

Now, as you observed:

$$\displaystyle R+A=1560\implies A=1560-R$$

And so we can now substitute into the first equation to get an equation in $$R$$ only:

$$\displaystyle R-50=5((1560-R)+50)$$

Solving this equation, you will indeed find $$R=1350$$.

MarkFL said:
After Raju gave Ann 50 dollars Raju had $$R-50$$ and Ann had $$A+50$$, so we want:

$$\displaystyle R-50=5(A+50)$$

Thank you for this.

When I went back to this question, I had a feeling that I was making math up. Thanks again.

## What is the formula for solving this problem?

The formula for solving this problem is: x = 5y, where x represents Raju's initial amount of money and y represents Ann's initial amount of money.

## Can this problem be solved using algebra?

Yes, this problem can be solved using algebra by setting up the equation x = 5y and solving for x.

## What is the importance of knowing the initial amount of money?

Knowing the initial amount of money is important because it allows us to determine the relationship between Raju's and Ann's money and find the solution to the problem.

## How can this problem be solved without using algebra?

This problem can be solved without using algebra by using a ratio and proportion method. We can set up the ratio 5:1 to represent Raju's money to Ann's money and then solve for the total amount by dividing the given total amount by 6.

## Can this problem be solved if the total amount of money is not given?

No, this problem cannot be solved without knowing the total amount of money. We need this information to determine the initial amounts of money for both Raju and Ann.

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