She has 47 nickels and 23 dimes.
Step-by-step explanation:
Worth of dimes and nickels = $4.65 = 4.65*100 = 465 cents
No. of coins = 70
1 nickel = 5 cents
1 dime = 10 cents
Let,
x be the number of nickels.
y be the number of dimes.
According to given statement;
x+y=70 Eqn 1
5x+10y=465 Eqn 2
Multiplying Eqn 1 by 5
[tex]5(x+y=70)\\5x+5y=350\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+10y)-(5x+5y)=465-350\\5x+10y-5x-5y=115\\5y=115\\[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{115}{5}\\y=23[/tex]
Putting y=23 in Eqn 1
[tex]x+23=70\\x=70-23\\x=47[/tex]
She has 47 nickels and 23 dimes.
Keywords: linear equation, elimination method
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