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17 May 2022, 20:38
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let A be the remaining amount after purchase of house.
then, (1/3)*A*(4/100)+(2/3)*A*(6/100) = 320
A/(3*100), common factor,
A/(3*100) *[4+12]=320
16A/(3*100) =320; A=320/16 *(3*100) =6000
Amount of house purchase = 100,000-6000 = 94,000 (E)
then, (1/3)*A*(4/100)+(2/3)*A*(6/100) = 320
A/(3*100), common factor,
A/(3*100) *[4+12]=320
16A/(3*100) =320; A=320/16 *(3*100) =6000
Amount of house purchase = 100,000-6000 = 94,000 (E)
14 Jun 2023, 10:30
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nalinnair
To determine the amount he invested, we can use the simple interest formula:
P × r × t = Interest
P is the invested amount, or principal.
r is the simple annual interest rate on his investment portfolio, which, in this case, is the weighted average of the given interest rates:
(1/3)4% + (2/3)6% = 16/3% = 16/300 (Remember that in the simple interest formula, we have to use the fraction or decimal form of the interest rate.)
t = 1, since the length of the investment period is 1 year.
P × 16/300 × 1 = $320
P = (320)(300)/16 = $6,000
Therefore, the purchase price of the house was:
$100,000 - $6,000 = $94,000
Answer: B
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09 Aug 2025, 15:11
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another good way of very quickly calculating this is to just try to find what amount is invested to get a return of $320 in interest.
Then once you have result you can subtract that value from $100,000 to get your house cost.
So
(a/3) * (4/100) + (2a/3) * (6/100) = 320
where a = total amount invested. We broke it up into one portion of 1/3 and second portion of 2/3
16a/3000 = 320
16a = 96000
a = 6000.
So 100,000 - 6000 = 94,000 Which is the price of the house.
If you recognize this, then its a simple 40 second question. Otherwise you would need to start plugging in
Then once you have result you can subtract that value from $100,000 to get your house cost.
So
(a/3) * (4/100) + (2a/3) * (6/100) = 320
where a = total amount invested. We broke it up into one portion of 1/3 and second portion of 2/3
16a/3000 = 320
16a = 96000
a = 6000.
So 100,000 - 6000 = 94,000 Which is the price of the house.
If you recognize this, then its a simple 40 second question. Otherwise you would need to start plugging in
