a box containing pens,nickels,and dimes has 13 coins with a total value of 83 cents.how many coins of each type are in the box?

Answer 1

number of pennies --- p
number of nickels ---- n
number of dimes ---- 13-p-n

p + 5n + 10(13-p-n) = 83
p + 5n + 130 - 10p - 10n = 83
-9p - 5n= -47
9p + 5n = 47 ---> n = (47-9p)/5
since both p and n have to be positive integers
0 < p < 5 and 0 < n< 10

try p=1 , n is a fraction
p = 2, n is a fraction
p=3 , n = 4
p = 4 , n is a fraction

so p = 3, n = 4 and subbing back, dimes = 6

check" 3(1) + 4(5) + 6(10) = 83