Help with algebraic math homework, easy 10 points!?

Question

Our Mathematics homework is due tomorrow and I have no idea how to do it! My parents do not know either, and it needs to be done otherwise I get an after school detention. The question is: I bought some nails and screws to finish a few home renovation projects. I did not buy the same number of nails and screws. I bought 250 nails and screws in total. If each nail costs 2 cents, each screw costs 12 cents and the total cost is $8.20, how many nails and screws did I buy?
I need two methods to solve this problem, If you get me started I should be able to work it out myself but I have no idea what to do! Thank you in advance!

Answer 1

Number of nails and screws  = 250

n +s = 250 ----------- (1)

But nail cost is 2cents, screw cost is 12cents and the total is $8.20

1$ =100 cents

$8.20 *100 = 820cents

2n+12s = 820 --------- (2)

multiple the equation (1) by 2

2n+2s = 500 ------------ (3)

eliminate the varible subtract (3) from (2)

2n+12s = 820

2n+2s = 500

(-)  (-)    (-)

_____________

10s = 320

s = 320/10

s = 32

Subtract the s value in (1)

n+32 = 250

n = 250-32

n = 218

screws = 32, nails = 218