word problem strategies

Question

Page 111 of Manhattan "Preeti has money in two separate bank accounts. Account X earns 8% interest annually and account Y earns 15% interest annually. Preeti earned a total of $53 in interest last year. If the total amount of money in the accounts at the beginning of last year was $400, and there were no other deposits or withdrawals,
how much money was in account Y?

i used weighted average technique , total interest she got is 13.25
then the two differentials are -5.25 and 2.25 
i.e (-5.25)x+(2.25)y=0
ratio is 3:7 
 but i mnt geting the correct answer

ans :amounts in banks X and Y are 300 and 100 respectively.

plz advice

KarishmaB · Answer

Its a calculation error - 5.25 and 1.75

Avg interest rate = 53/4 (I don't like to use decimals)
Two rates are 32/4 and 60/4
Ratio is 7:21 i.e. 1:3
So $100 in account X and $300 in account Y.

nevagivup · Answer

thanku so much for ur reply .(as.being impatient , its very hard fr me to move on the next page :-D

)

arsalansyed21 · Answer

ScottTargetTestPrep · Answer

Solution:

Let x be the amount of money in Account X. Then, the amount of money in Account Y is 400 - x. Since Account X pays 8% interest, the interest earned from Account X at the end of the year is 0.08x. Similarly, since Account Y pays 15% interest, the interest earned from Account Y at the end of the year is 0.15(400 - x). We are told that the total amount of interest earned from both accounts is $53, so:

0.08x + 0.15(400 - x) = 53

0.08x + 0.15*400 - 0.15x = 53

60 - 0.07x = 53

7 = 0.07x

x = 7/0.07 = 100

So, x = $100 was in Account X and 400 - x = $300 was in Account Y.

Answer: 300

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