My bag contains $7.50 in nickels and dimes. There are 6 more dimes than nickels. Find the number of dimes and nickels

Question

i need  help  figuring out this problem

Answer 1

If we make x the number of nickels, we can write the following equation:

 

10(x+6) + 5x = 750

10x + 60 + 5x = 750

15x + 60= 750

-60            -60

15x = 690

___    ___

15       15

x    =   46

 

So, x = 46, the nickles.

If there are 6 more dimes than nickels: 46 + 6 = 52

 

52 x .10 = 5.20

46 x .05 = 2.30

____________

                7.50

 

To check we can plug x (nickels) into our original equation:

10(46 +6) + 5(46)

10(52) + 5(46)

 520 + 230 = 750

Answer 2

Hi Diamond,

 

This problem involves some algebraic substitution.

 

1) First, let's define the scenario in the form of an equation. Each nickel is worth $0.05, each dime is worth $0.10, and the total amount in the bag is $7.50:

 

.05n + .10d = 7.50

 

 

2) Next, let's use the information given in the problem to remove one of our variables. There are 6 more dimes than nickels in the bag, so we can define the number of dimes in terms of the number of nickels:

 

d = n+6

 

 

3) Now, we can substitute this definition of d for the original variable in our equation, giving us:

 

.05n + .10(n+6) = 7.50

 

 

4) Next, we can distribute to simplify:

 

.05n + .10n + .6 = 7.50

 

 

5) We can now combine "like terms" and solve for n:

 

.15n = 6.9

 

.15n/.15 = 6.9/.15

 

n = 46

 

 

6) We have 46 nickels! Let's plug this information into our formula for dimes:

 

d = n+6

 

d = (46)+6

 

d = 52

 

 

7) Done! We have 46 nickels and 52 dimes, giving us a total of $7.50 in the bag.

 

 

Good luck!

 

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