 Carol Gates

2021-02-16

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. ### Answer & Explanation Faiza Fuller Skilled2021-02-17Added 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.

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