Question

help!! we are learning ‘applying systems of equations’ and i don’t understand it! Please, please please help!

Answer 1

Answer:

Step-by-step explanation:

This type of problem requires you to identify what the unknown quantities are and then to set up your own equations to find their values algebraically.

In the above problem, there are two people, Troy and Caitlin.  Let t represent Troy's earnings and c represent Caitlin's.  The problem asks us to find the value of t.

"Caitlin earned $5 more than twice what Troy earned," translated into a symbolic equation, would be  c = 2t + $5.

"The sum of their earnings was $80" translates into c + t = $80.

We need to solve this "system of linear equations."  One way of doing that is by substitution; we see that c = 2t + $5.  Thus, 2t + $5 can be subbed for c in the equation c + t = $80:

2t + $5 + t = $80

We need to solve this equation for t.

Combining the "t" terms results in 3t + $5 = $80.

Subtracting $5 from both sides results in 3t = $75.

Dividing both sides of this result yields t = $25.

We have to come to conclusions and share them in a sentence or two:

Troy earned $25.  Caitlin, who earned twice as much as Troy, plus $5, earned 2($25) + $5, or $55.

We check this by determining whether that $55 and that $25 add up to $80.  They do!

You must mimic the language of the problem in writing out your answer:  "Caitlin earned $55 last month."