algebra word problem

Question

Phil has 50 nickels and dimes worth $4.15. How many dimes does he have?

Answer 1

We solve this using a system of equations. We'll use the variables

n, to represent the number of nickels

d, to represent the number of dimes

How many coins are there?

n + d = 50

5n, is the value of the nickels

10d is the value of the dimes

415 cents is the total value

What is the total value?

5n + 10d = 415

Since it is easy to solve the first equation for a variable, I would use the substitution method to solve the system:

n + d = 50

5n + 10d = 415

n = 50 - d

5n + 10d = 415

SUBSTITUTE:

5(50-d) + 10d = 415

250 - 5d + 10d = 415

Continue to solve for d and then substitute that value into any of the original equations to get n

Answer 2

D + N = 50

multiply by 10

10D + 10N = 500

10D + 5N = 415

subtract 2nd equation from 1st

5N = 85

N = 17 nickels

D+N = 50

D + 17 = 50

D = 50-17 = 33 dimes

5(17) + 10(33) = 85 + 330 = $4.15