Question

Please help! provide thorough explanation and use elimination method!!

Answer 1

Multiply both sides of the second equation by 100 to get rid of the decimals:

0.05n + 0.10d = 1.50

==>  5n + 10d = 150

Multiply both sides of the first equation by -5:

n + d = 21

==>  -5n - 5d = -105

Add the two equations together:

(5n + 10d) + (-5n - 5d) = 150 + (-105)

Notice that the terms containing n get eliminated and we can solve for d :

(5n - 5n) + (10d - 5d) = 150 - 105

5d = 45

d = 45/5 = 9

Plug this into either original equation to solve for n. Doing this with the first equation is easiest:

n + 9 = 21

n = 21 - 9 = 12

So Donna used 12 nickels and 9 dimes.