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. chase purchased 23 shares in the software company and 88 shares in the biotech firm, which cost a total of $4,539. at the same time, sophie invested a total of $2,823 in 23 shares in the software company and 49 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: Set up equations

Let \(x\) be the cost per share of the software company and \(y\) be the cost per share of the biotech firm.
For Chase: \(23x + 88y=4539\)
For Sophie: \(23x+49y = 2823\)

Step2: Subtract the second equation from the first

\((23x + 88y)-(23x + 49y)=4539 - 2823\)
\(23x-23x+88y - 49y=1716\)
\(39y=1716\)
\(y=\frac{1716}{39}=44\)

Step3: Substitute \(y = 44\) into the second equation

\(23x+49\times44=2823\)
\(23x+2156=2823\)
\(23x=2823 - 2156\)
\(23x=667\)
\(x=\frac{667}{23}=29\)

Answer:

Each share in the software company cost \(\$29\), and each share in the biotech firm cost \(\$44\).