Question

LearningDiagnosticAnalyticsRecommendationsSkill plansMath09 Language artsScienceSocial studiesTX StandardsAlgebra 14.11 Solve a system of equations using elimination: word problems NHRYou have prizes to reveal! Go to yourWrite a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.For a project in statistics class, a pair of students decided to invest in two companies, onethat produces software and one that does biotechnology research. Regan purchased 59shares in the software company and 68 shares in the biotech firm, which cost a total of$6,538. At the same time, Turner invested a total of $8,722 in 59 shares in the softwarecompany and 94 shares in the biotech firm. How much did each share cost?00and each share in the biotech firm costEach share in the software company cost $$SmOueSubmit

Answer 1

Let x be the price of the software company shares and y be the price of the biotech firm shares. We are told that regan purchased 59 shares of the software company and 68 shares of the biotech company and that that totals 6538. Recall that the cost of 59 shares of the software company would be

`59\cdot x`

and the cost of 68 shares of the biotech company would be

`68y`

if we add these two quantities, we should get the total cost. Then we get the equation

`59x+68y=6538`

Following the same principle for Turner's investment, we get the equation

`59x+94y=8722`

Now, we want to solve this system of equations. We see that both equations have 59x. So, let us subtract the first equation from the second one, we get

`59x+94y\text{ - (59x+68y)=59x -59x+94y - 68y = 26y = 8722 - 6538 = 2184}`

which is the equation

`26y=2184`

Now, we divide both sides by 26, so we get

`y=(2184)/(26)=84`

Then, the price per share of the Biotech company is 84

Let us replace this value in the first equation, we get

`59x+68y=59x+68\cdot84=59x+5712=6538`

if we subtract 5712 from both sides, we get

`59x=6538\text{ -5712}=826`

Finally, we divide both sides by 59, so we get

`x=(826)/(59)=14`

Then, the price per share of the software company is 14