Answer:
The number of nickels are 16 and the number of dimes are 14.
Step-by-step explanation:
As given
Let n represent the number of nickels.
let d represent the number of dimes.
As given
Luis is saving money to purchase a new video game.
He has a total of 30 coins consisting of nickels and dimes.
Than the equation becomes
n + d = 30
As the value of the coins is $2.20.
As 1 nickel = 0.05 dollars
1 dimes = 0.1 dollars
Than the equation becomes
0.05n + 0.1d = 2.20
Simplify the above
[tex]\frac{5n}{100} +\frac{d}{10} = \frac{220}{100}[/tex]
L.C.M of (10,100) = 100
Than
5n + 10d = 220
Than two equations are
n + d = 30 and 5n + 10d = 220
Multiply n + d = 30 by 5 and subtracted from 5n + 10d = 220 .
5n - 5n + 10d - 5d = 220 - 150
5d = 70
[tex]d = \frac{70}{5}[/tex]
d = 14
Put in the equation n + d = 30
n + 14 = 30
n = 30 - 14
n = 16
Therefore the number of nickels are 16 and the number of dimes are 14.
