Question 620589
I have some change (pennies, nickels, and dimes) in my pocket.
 Fourteen of the coins are dimes, 25% of them are nickels, and five-ninths of them are pennies.
 What is the total value of my change?
:
Let p = no. of pennies
Let n = no. of nickels
no. of dimes given as 14
Let t = total number of coins
:
Find the total number coins first
:
"25% of them are nickels,"
n = {{{1/4}}}t
:
"five-ninths of them are pennies."
p = {{{5/9}}}t
:
t = p + n + 14
Replace p and n
t = {{{5/9}}}t + {{{1/4}}}t + 14
multiply by 36 to clear the denominators, results
36t = 4(5t) + 9t + 36(14)
36t = 20t + 9t + 504
36t = 29t + 504
36t - 29t = 502
7t = 504
t = 504/7
t = 72 coins
then
p = {{{5/9}}}(72)
p = 40 pennies
and
n = {{{1/4}}}(72)
n = 18 nickels
:
" What is the total value of my change?"
V = .01(40) + .05(18) + .10(14)
V = .40 + .90 + 1.40
V = $2.70