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Mr. Tally inherited $200,000. He used a portion of the inheritance to build a house. He invested the rest of the money for one year as follows: 1/3 at 12% and 2/3 at 15%. The interest from both investment was $8,400. How much did it cost to build the house?

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Amount inherited = $200,000

Portion used to build house = h

Invested amount = 200,000 - h

1/3 of (200,000 - h) was invested at 12%

2/3 of 200,000 - h was invested at 15%

Interest from both investment = 8400

Cost of building =?

Using the simple interest formula :

Principal(P) * rate(r) * time

If the investment was for a year:

1st investment :

(200,000 - h)/3 * 0.12 * 1 = (24000 - 0.12h) / 3 = (8000 - 0.04h)

2nd :

(200,000 - h)*2/3* 0.15 * 1 = (20,000 - 0.1h)

Summing both :

8000 - 0.04h + 20,000 - 0.1h = 8400

28000 - 0.14h = 8400

-0.14h = 8400 - 28000

-0.14h = - 19600

= 140,000

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