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

Carol Gates 2021-02-16 Answered
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.
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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 (25x+10y) 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=60x
Plug this in 25x+10y=945 and solve for x.
25x+10y=945
25x+10(60x)=945
25x+60010x=945
15x=945600
15x=345
x=34515
x=23
y=60x
y=6023
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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