A bank teller knows that she received 34 dimes and nickels from a customer. If the change totaled $2.05, how many dimes and nickels did she receive?

D = # of dimes

n = # of nickles

d + n = 34 so d = 34 - n

.10d +.05n = 2.05

substitute d = 34 - n into. 10d +.05n = 2.05

.10d +.05n = 2.05

.10 (34 - n) +.05n = 2.05

3.4 -.1n +.05n = 2.05

-.05n = - 1.35

n = 27

d = 34 - n

d = 34 - 27

d = 7

answer

she received 7 dimes and 27 nickels