Answer:
Emily has 12 dimes and 8 nickels.
Step-by-step explanation:
Emily has a total of 20 coins.
Let d be the number of dimes she has and n the number of nickels:
[tex]d + n = 20\\d= 20 - n[/tex]
Dimes are worth 10 cents and nickels are worth 5 cents, therefore the amount she has and what she would have if the dimes were nickels and nickels were dimes are, respectively:
[tex]d*10 + n*5\\d*5 + n*10[/tex]
Since she would have 20 cents less in the second option, the following equation can be written:
[tex]d*10 + n*5 = d*5 + n*10 + 20\\5(20-n) - 5n = 20[/tex]
Substituting (d = 20 - n) into this equation yields:
[tex]5(20-n) - 5n = 20\\10n=80\\n=8\\d=20 - 8\\d = 12[/tex]
Emily has 12 dimes and 8 nickels.
