Question

Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 2 times as many dimes as nickels, and the value of the dimes is $1.05 more than the value of the nickels. How many nickels and dimes does Jamil have?

Answer 1

7 nickels and 14 dimes

Explanation:

In tricky word problems like this you have to translate the word problem to algebraic equations

Let number of nickels = N
Let number of dimes = D

2 times as many nickels as dimes is saying that
the nmber of dimes = twice the number of nickels
and translates to D = 2N (1)

Value of D dimes = 10D cents since each dime is 10 cents
Value of N nickels = 5N cents since each nickel is 5 cents

$1.05 = 105 cents

So,

Value of dimes is $1.05 more than value of nickels translates to :

10D - 5N = 105 (2)

Since we have D = 2N we can use this relation to substitute for the value of D in terms of N
10D - 5N ==> 10(2N) - 5N = 20N - 5N = 15N

From (2) we get
15N = 105

N = 105/15 = 7
So there are 7 nickels

D = 2N = 2 x 7 = 14
So there are 14 dimes

Hence there are 7 nickels and 14 dimes

Let's check and see if our answer is right by plugging this value into the second equation

10D - 5N = 10 x 14 - 5 x 7 = 140 - 35 = 105 cents =$1.05