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The expression $1.05S + 1.02B$ predicts the end-of-year value of a financial portfolio, where $S$ is the value of stocks in dollars and $B$ is the value of bonds in dollars in the portfolio at the beginning of the year. What is the predicted end-of-year value, in dollars, of a portfolio that begins the year with $S$ dollars in stocks and $B$ dollars in bonds?

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Evaluate two-variable equations: word problems

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Q. The expression

1.05S + 1.02B

predicts the end-of-year value of a financial portfolio, where

S

is the value of stocks in dollars and

B

is the value of bonds in dollars in the portfolio at the beginning of the year. What is the predicted end-of-year value, in dollars, of a portfolio that begins the year with

S

dollars in stocks and

B

dollars in bonds?

Identify expression: Identify the expression for the end-of-year value. The expression is $1.1x + 1.05y$ , where $x$ is the value of stocks and $y$ is the value of bonds at the beginning of the year.
Substitute values: Substitute the given values into the expression. Assume $x = 5000$ dollars and $y = 3000$ dollars. Calculate $1.1 \times 5000 + 1.05 \times 3000$ .
Perform calculations: Perform the calculations: $1.1 \times 5000 = 5500$ and $1.05 \times 3000 = 3150$ .
Add results: Add the results of the calculations: $5500 + 3150 = 8650$ .

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