Question

Joe has a collection of nickels and dimes that is worth $6.20. If the number of dimes was doubled and the number of nickels was decreased by 7, the value of the coins would be $10.35. How many nickels and dimes does he have?

Answer 1

$6.20 = 620 cents
a: number of nickels
b: number of dimes
\[5a+10b = 620\]
\[5(a-7)+10(2b)=1035\]\[5a-35+20b=1035\]\[5a+20b=1070\]
Two equations
\[5a+20b=1070\]\[5a+10b=620\]
Subtract.
\[10b=450\]\[b=45\]
Plug in b to get a.
\[5a+450=620\]\[5a=170\]\[a=34\]

a=34, b=45