Question 175614: Sally has seven times as many dimes as nickels. Their value is $3.00. How many nickels does she have? Found 3 solutions by EMStelley, Mathtut, solver91311:Answer by EMStelley(208) (Show Source):
You can put this solution on YOUR website! Call the number of nickels n. Then the number of dimes is 7n. The value of the amount of nickels is 0.05n because each nickel is worth $0.05. Thus the value of the amount of dimes is 0.10(7n) for the same reason.
So
Thus Sally has 4 nickels and 28 dimes.
You can put this solution on YOUR website! lets call the # of dimes and nickels , d and m, respectively
:
d=7n.....eq 1
.1d+.05n=3....eq 2
:
take d's value of 7n in eq 1 and plug it into eq 2
:
.1(7n)+.05n=3
:
.75n=3
: nickels
: dimes
We know that because Sally has seven times as many dimes as nickels.
Each of Sally's nickels is worth 5 cents, so the value, in cents, of all of Sally's nickels is . Likewise, the value, in cents, of all of Sally's dimes is .
We know that the total value of Sally's coins is $3.00, but we can also say that the total value of her coins is 300 cents. Now we can write:
But since we also know that , we can substitute for :
Solving:
Therefore Sally has 4 nickels.
Check: If Sally has 4 nickels, she must have dimes. 28 dimes are worth $2.80 and 4 nickels are worth $0.20 and $2.80 plus $0.20 is $3.00. Answer checks.
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