Question

write a system of equations to describe the situation below, solve using any method, and fill in the blanks. 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. natalie purchased 59 shares in the software company and 11 shares in the biotech firm, which cost a total of $2,247. at the same time, shivani invested a total of $8,892 in 76 shares in the software company and 76 shares in the biotech firm. how much did each share cost? each share in the software company cost $ , and each share in the biotech firm cost $ .

Explanation:

Step1: Define variables

Let $x$ be the cost of a share in the software - company and $y$ be the cost of a share in the biotech firm.
Natalie's investment gives the equation $59x + 11y=2247$.
Shivani's investment gives the equation $76x + 76y=8892$.
We can simplify the second equation by dividing throughout by 76: $x + y = 117$, so $y=117 - x$.

Step2: Substitute $y$ into the first equation

Substitute $y = 117 - x$ into $59x+11y = 2247$.
$59x+11(117 - x)=2247$.
Expand the left - hand side: $59x+1287-11x = 2247$.
Combine like terms: $(59x - 11x)+1287 = 2247$.
$48x+1287 = 2247$.

Step3: Solve for $x$

Subtract 1287 from both sides: $48x=2247 - 1287$.
$48x = 960$.
Divide both sides by 48: $x=\frac{960}{48}=20$.

Step4: Solve for $y$

Substitute $x = 20$ into $y = 117 - x$.
$y=117 - 20=97$.

Answer:

20, 97