A man has ​$380 comma 000 invested in three rental properties. One property earns 6.5​% per year on the​ investment, the second earns 9​%, and the third earns 8​%. The total annual earnings from the three properties is $ 30 comma 550​, and the amount invested at 8​% equals the sum of the first two investments. Let x equal the investment at 6.5​%, y equal the investment at 9​%, and z represent the investment at 8​%.

Question

Complete parts​ (a) through​ (d) below.
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Part 1
a. Write an equation that represents the sum of the three investments.
  
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​(Type an equation. Do not include the​ $ symbol in your​ answer.)

Answer 1

To represent the sum of the three investments, we can set up the following equation based on the information provided:

Given:

• Total investment: \( 380000 \)
• Investments: \( x \) (6.5%), \( y \) (9%), and \( z \) (8%)

The equation for the total sum of the investments will be:

\[ x + y + z = 380000 \]

So, the equation representing the sum of the three investments is:

\[ x + y + z = 380000 \]