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

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Raju and Ann saved a total of $1560, with Raju initially having five times as much money as Ann after giving her $50. The equations established were R + A = 1560 and R - 50 = 5(A + 50). By substituting A with (1560 - R) in the second equation, it was determined that R = 1350. Thus, Raju initially had $1350 before giving Ann $50. The calculations confirmed the solution and clarified any confusion regarding the math involved.
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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.
 
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After Raju gave Ann 50 dollars Raju had \(R-50\) and Ann had \(A+50\), so we want:

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

Now, as you observed:

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

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

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

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:

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

Thank you for this.

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