Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]
Step-by-step explanation:
Given information
Number of coins = 24 coins
Total amount = $1.95
Dime = 10 cents = $0.1
Nickel = 5 cents = $0.05
Set variables
Let d be the number of dimes
Let n be the number of nickels
Set a system of equation
1) d + n = 24
2) 0.1d + 0.05n = 1.95
Multiply 10 on both sides of 2) equation
0.1d · 10 + 0.05n · 10 = 1.95 · 10
d + 0.5n = 19.5
Current system
1) d + n = 24
2) d + 0.5n = 19.5
Subtract 2) equation from the 1) equation
(d + n) - (d + 0.5n) = (24) - (19.5)
Expand the parenthesis
d + n - d - 0.5n = 24 - 19.5
Combine like terms
d - d + n - 0.5n = 4.5
0.5n = 4.5
Divide 0.5 on both sides
0.5n / 0.5 = 4.5 / 0.5
[tex]\Large\boxed{n=9}[/tex]
Substitute the n value into one of the equations to find the d value
d + n = 24
d + (9) = 24
d = 24 - 9
[tex]\Large\boxed{d=15}[/tex]
Hope this helps!! :)
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