Question 56836: I really dont get how to do this. Here it is- Jacob has $3.50 in nickels and dimes. He has twice as many dimes as nickels. How many nickels and how many dimes does he have?
Found 2 solutions by checkley71, mszlmb:
Answer by checkley71(8403)   (Show Source):
Answer by mszlmb(115)  (Show Source):
You can put this solution on YOUR website! "I really dont get how to do this. Here it is- Jacob has $3.50 in nickels and dimes. He has twice as many dimes as nickels. How many nickels and how many dimes does he have?"
.05N+.1D=3.50
D=2N
How did I obtain the first equation? Every nickel is 5 cents, which is .05 dollars; and every dime has 10 cents, which is .1 dollars. The number of nickels (N) times a nickel's worth will give you the total worth of the nickels. Similarily, the dime is worth .1 dollars, so the number of dimes (D) times its worth in dollars (.1) will equal the total worth.
So you're keeping up, but how did I get the second equation? It says that there are "twice as many dimes as nickels", so shouldn't 2D=N? No. If 2D equaled N, then D would have to be twice as much as N. Whilst 2N=D, however, it is clear that N is half D (which is the same thing as saying that D is twice N)
Finally we combine the equations.
Since 2N=D, we can replace D [the number of dimes] in the first equation with its equivalent, 2N. The first equation yields:
.05N+.1(2N)=3.50 simplify:
.05N+.2N=3.50 simplify further
.25N=3.50 Divide both sides by .25
N=14 There are 14 nickels.
Plug this in to the second equation
D=2N :
D=2(14)
D=28
There are 28 Dimes and 14 Nickels.
let's check: Are there twice as many dimes as nickels? 28/2=14, so ya.
Are 28 dimes + 14 nickles equal to $3.50?
28(.1)+14(.05)=3.5, or $3.50
Looks like we're clear
IM or EMAIl me for questions.
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