1. The average value of all the pennies, nickels, dimes,and quarters in Paula\'s

Question

1. The average value of all the pennies, nickels, dimes,and quarters in Paula's purse is 20 cents. If she had onemore quarter, the average value would be 21 cents. How manydimes does she have in her purse?     A)0      B)1       C)2           D)3       E)4 1. The average value of all the pennies, nickels, dimes,and quarters in Paula's purse is 20 cents. If she had onemore quarter, the average value would be 21 cents. How manydimes does she have in her purse?     A)0      B)1       C)2           D)3       E)4

Explanation / Answer

You need the following two equations. T = total sum of the coins N = number of coins T/N = 20, an average is the total value divided by the number ofcoins (T + 25) / (N + 1) = 21 : this is what happens when you add aquater do the algebra t + 25 = 21 (N+1) T + 25 = 21N + 21 T = 21N - 4 then you substitute this back into the other equation T/N = 20 (21N - 4)/N = 20 do the algebra 21N - 4 = 20N N = 4 this is the number of coins substitute back to get the value of the coins you have T/4 = 20, there is 80 cents at the start with 4 coins, you have 3quarters and 1 nickle put these numbers into the second equation to see if they work (80 + 25) / (4 + 1) = 105/5 = 21 cents, so you have 0 dimes

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