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xokatexo
1. Joy has 3 times as many dimes as nickels. In all she has $1.40, how many coins of each type does she have? 2. Vicki has $2.80 in quarters and dimes. The number of dimes is 7 less than the number of quarters. Find the number she has of each kind. 3. A purse containing $3.20 in quarters and dimes has, in all, 20 coins. Find the number of each kind of coin.
1. To compute the value of dimes and nickels you create a system of equations. Let's assume we have one variable that represents dimes 'd', and one variable for nickels 'n'. Now, we know that the total amount of dimes and nickels is $1.40. We know that a dime is $0.1 and a nickel is $0.05. Now we form the first equation, 0.1d+0.05n=1.4 And now from the second condition, namely the fact that we have 3 times as many dimes as nickels, we form the equation, d=3n We replace that, in the first equation, 0.1(3n)+0.05n=1.4 0.3n+0.05n=1.4 0.35n=1.4 n=1.4/0.35=4 So we have 4 nickels. And from the fact that we have 3 times as many dimes, we compute. d=3*4=12 dimes. Proof: 12*$0.1+4*$0.05=$1.2+$0.2=$1.4 Do the same logic with the other problems. :)