Answer:
nickles =17
dimes = 15
Step-by-step explanation:
nicklels =17 * 5 = .85
dimes = 15 * 10 = 1.50
1.50+.85=2.35
From the system of equations, the number of nickel coins are 17 and the number of dime coins are 15.
A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.
For the given situation,
A bill of $2.35 was paid in dimes and nickels.
Total number of coins = 32
A nickel is worth 5 cents and a dime is worth 10 cents.
1 nickel = 5 cents
1 dime = 10 cents
Let n be the nickel and
Let d be the dime
This can be write as system of equations as
[tex]0.05n+0.10d=2.35[/tex] ------ (1)
[tex]n+d=32[/tex] ------- (2)
From equation 2,
⇒ [tex]n=32-d[/tex]
Now substitute n in equation 1, we get
⇒ [tex]0.05(32-d)+0.10d=2.35[/tex]
⇒ [tex]1.6-0.05d+0.10d=2.35[/tex]
⇒ [tex]0.10d-0.05d=2.35-1.6[/tex]
⇒ [tex]0.05d=0.75[/tex]
⇒ [tex]d=15[/tex]
Substitute d in equation 2, we get
⇒ [tex]n+15=32[/tex]
⇒ [tex]n=32-15[/tex]
⇒ [tex]n=17[/tex]
Hence we can conclude that from the system of equations, the number of nickel coins are 17 and the number of dime coins are 15.
Learn more about the system of equations here
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