In a collection of nickels and dimes the number of dimes is 3 more than twice the number of nickels. If the total value is 1.80, how many nickels are there?

Question

I dont understand how to set up and solve the problem.  So if there was any way anyone could help and give me a step by step explanation that would be great.  I really need it soon!!

Answer 1

Translating is often the hard part.
First, identify the quantities involved
Let n be the number of nickels
Let d be the number of dimes
Second translate the words into equations.
The first sentence says that “the number of dimes is 3 more than twice the number of nickels” now we can translate the names:
“d is 3 more than twice n”
What does “twice n” mean? It means 2 * n, so, further translation
“d is 3 more than 2n”
What does “is 3 more”? It means addition,
“d = 3+2n”

Now the second .sentence is simpler.
“The total value is 1.80”
What is the total value? It’s the value of the dimes plus the value of the nickels.
What is the value of the dimes? It’s the value of one dimes times the number of dimes. What is the value of a dime? .10 dollars. So the value of dimes is .10 * d.
And the value of nickels is .05 * n.
Finally the total value is .10d + .05n.
So the second equation is
1.80 = .10d + .05n
d = 3+2n
So this is a pair of equations to solve for two variables. Probably you know how to do that?