There are 47 dimes and 23 quarters.
Step-by-step explanation:
Total amount = $10.45 = 10.45*100 = 1045 cents
Total coins = 70
1 dime = 10 cents
1 quarter = 25 cents
Let,
Dimes = x
Quarters = y
According to given statement;
x+y=70 Eqn 1
10x+25y=1045 Eqn 2
Multiplying Eqn 1 by 10;
[tex]10(x+y=70)\\10x+10y=700\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](10x+25y)-(10x+10y)=1045-700\\10x+25y-10x-10y=345\\15y=345[/tex]
Dividing both sides by 15;
[tex]\frac{15y}{15}=\frac{345}{15}\\y=23[/tex]
Putting y=23 in Eqn 1
[tex]x+23=70\\x=70-23\\x=47[/tex]
There are 47 dimes and 23 quarters.
Keywords: linear equations, subtraction
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