Lea just emptied her piggy bank and found that she had $2.85 in nickels and dimes. If the number of nickels is 1 more than twice the number

Lea just emptied her piggy bank and found that she had $2.85 in nickels and dimes. If the number of nickels is 1 more than twice the number of dimes, how many nickels did she have in her piggy bank?

Call the number of dimes , x

Call the number of nickels 2x + 1

So we have, the number of nickels times their value plus the number of dimes times their value = the total value....algebraically, this is....

.05(2x + 1)  + .10x  = 2.85     multiply through by 100 to clear the decimals

5(2x + 1) + 10x = 285             simplify

10x + 5 + 10x = 285   

20x + 5 = 285                        subtract 5 from both sides

20x = 280                              divide by 20 on each side

x = 14    = number of dimes

2(14) + 1  = 29 = number of nickels