MATH SOLVE

5 months ago

Q:
# a collection of dimes and nickels is worth $4.70 there are 60 coins in all how many of each are there?

Accepted Solution

A:

Answer:26 nickels34 dimesStep-by-step explanation:If all were nickels, the value would be 60Γ$0.05 = $3.00. Their $4.70 value is $1.70 more than that. For each nickel replaced by a dime, the value goes up by $0.05, so there must be 1.70/0.05 = 34 replacements. That is, ...... there are 34 dimes and 60-34 = 26 nickels._____Using an equationIn mixture problems, it often works well to let the variable represent the quantity of the largest contributor. Here, we can let "d" represent the number of dimes, the coin with the greatest value. Then 60-d will be the number of nickels, and the total value of the coins (in dollars) is ...... (60 -d)Γ0.05 + dΓ0.10 = 4.70... 0.05d + 0.05Γ60 = 4.70 . . .simplify... 0.05d = 4.70 -3.00 . . . . . . . subtract 3.00... d = 1.70/0.05 = 34 . . . . . . . . divide by the coefficient of dThere are 34 dimes and 26 nickels.The sequence of math steps should look a lot like the sequence of steps described in words, above._____As a mixture problemThe average coin value is 4.70/60 = 0.07833... = 7 5/6Β’. Then the proportion that are dimes is given by ...... (7 5/6 - 5)/(10 - 5) = (2 5/6)/5 = 17/30 . . . . . 10 and 5 are the cents values of the coins in the mixMultiplying by the 60 coins, we find (17/30)Γ60 = 34 are dimes. The remaining 26 are nickels.- - - The formula used above is ...... proportion of highest contributor = ...... ((mix value) - (least contributor)) / ((greatest contributor) - (least contributor))This is the generic solution for any mixture problem.