Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Maddie purchased $79$ shares in the software company and $20$ shares in the biotech firm, which cost a total of $\$3,813$ . At the same time, Dave invested a total of $\$1,977$ in $11$ shares in the software company and $20$ shares in the biotech firm. How much did each share cost? $\newline$ Each share in the software company cost $\$\_\_\_\_$ , and each share in the biotech firm cost $\$\_\_\_\_$ .

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Solve a system of equations using any method: word problems

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Maddie purchased

79

shares in the software company and

20

shares in the biotech firm, which cost a total of

\$3,813

. At the same time, Dave invested a total of

\$1,977

11

shares in the software company and

20

shares in the biotech firm. How much did each share cost?

\newline

Each share in the software company cost

\$\_\_\_\_

, and each share in the biotech firm cost

\$\_\_\_\_

Define Share Costs: Let's denote the cost of one share in the software company as $x$ dollars and the cost of one share in the biotech firm as $y$ dollars.
Maddie's Investment Equation: Maddie's investment can be represented by the equation $79x + 20y = 3813$ , as she bought $79$ shares of software and $20$ shares of biotech.
Dave's Investment Equation: Dave's investment can be represented by the equation $11x + 20y = 1977$ , as he bought $11$ shares of software and $20$ shares of biotech.
System of Equations: We now have a system of equations to solve: $\newline$ $79x + 20y = 3813$ $\newline$ $11x + 20y = 1977$
Eliminate Variable $y$ : To eliminate $y$ , we can subtract the second equation from the first: $\newline$ $(79x + 20y) - (11x + 20y) = 3813 - 1977$ $\newline$ $79x - 11x = 3813 - 1977$ $\newline$ $68x = 1836$
Solve for x: Solving for x, we divide both sides by $68$ : $x = \frac{1836}{68}$ $x = 27$
Substitute $x$ into Equation: Now that we have the value of $x$ , we can substitute it back into one of the original equations to solve for $y$ . Let's use the second equation: $\newline$ $11(27) + 20y = 1977$ $\newline$ $297 + 20y = 1977$
Solve for y: Subtract $297$ from both sides to solve for y: $\newline$ $20y = 1977 - 297$ $\newline$ $20y = 1680$
Solve for y: Subtract $297$ from both sides to solve for $y$ : $\newline$ $20y = 1977 - 297$ $\newline$ $20y = 1680$ Divide both sides by $20$ to find the value of $y$ : $\newline$ $y = \frac{1680}{20}$ $\newline$ $y = 84$