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 total amount of coins be A


¼ of coins are nickels


{{{5/9}}} of coins are pennies


Therefore, fraction of coins that are dimes = {{{1 - (1/4 + 5/9))}}}, or {{{1 - 29/36}}}, or {{{7/36}}}


Now, since amount of dimes = 14, then we can say that: {{{7/36 = 14}}}, and also that: {{{(7/36)/1 = 14/A}}}


{{{A(7/36) = 14}}} ----- Cross-multiplying


{{{7A/36 = 14}}}

 
7A = 504 ------ Cross-multiplying


A, or total amount of coins = {{{504/7}}}, or 72


14 dimes = $1.40


Amount of nickels = {{{1/4}}} of 72, or 18, for a value of $0.90


Amount of pennies = {{{5/9}}} of 72, or 40, for a value of $0.40


Total value of change = $1.40 + 0.90 + 0.40 = ${{{highlight_green(2.70)}}}


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