Question

Solve each system of equations by using substitution

Answer 1

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:

$d + n = 20\\d= 20 - n$

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:

$d*10 + n*5\\d*5 + n*10$

Since she would have 20 cents less in the second option, the following equation can be written:

$d*10 + n*5 = d*5 + n*10 + 20\\5(20-n) - 5n = 20$

Substituting (d = 20 - n) into this equation yields:

$5(20-n) - 5n = 20\\10n=80\\n=8\\d=20 - 8\\d = 12$

Emily has 12 dimes and 8 nickels.