# When solving systems of equations we have at least two unknowns. A common example of a system of equations is a price problem. For example, Jacob has

When solving systems of equations we have at least two unknowns. A common example of a system of equations is a price problem. For example, Jacob has 60 coins consisting of quarters and dimes.
The coins combined value is $9.45. Find out how many of each (quarters and dimes) Jacob has. 1.What do the unknowns in this system represent and what are the two equations that that need to be solved? 2.Finally, solve the system of equations. You can still ask an expert for help Expert Community at Your Service • Live experts 24/7 • Questions are typically answered in as fast as 30 minutes • Personalized clear answers Solve your problem for the price of one coffee • Available 24/7 • Math expert for every subject • Pay only if we can solve it ## Expert Answer Faiza Fuller Answered 2021-02-17 Author has 108 answers Step 1 Let he has x quarters and y dimes He has total 60 coins So, $x+y=60$ Step 2 1 quarter $=25$ cents So, x quarters $=25x$ cents 1 dime$=10$ cents y dime$=10y$ cents Total $\left(25x+10y\right)$ cents He has total$9.45 or 945 cents
So, $25x+10y=945$
Step 3
Then solve these two equations: $x+y=60$ and $25x+10y=945$
From $x+y=60$ we get $y=60-x$
Plug this in $25x+10y=945$ and solve for x.
$25x+10y=945$
$25x+10\left(60-x\right)=945$
$25x+600-10x=945$
$15x=945-600$
$15x=345$
$x=\frac{345}{15}$
$x=23$
$y=60-x$
$y=60-23$
$y=37$
Result(1):Two unknowns are x and y. Where $x=$ number of quarters and $y=$ number of dimes.
$x+y=60$ and $25x+10y=945$ needs to be solved.
Result(2): He has 23 quarters and 37 dimes.