how do i find the formula for this

Question

A coin collection has 18 coins consisting of quarters and dimes. There are two more dimes than the number of quarters.If the face value of the collection is $3.00, how many quarters are in the collection?

Answer 1

In actuality, the face value of the total coins in dollars was not necessary information.

We know there are 18 coins total between quarters and dimes, and there are 2 more

dimes than quarters.

 

Q + D = 18          letting Q= # quarters,  D = # dimes

D = Q + 2           since there are 2 more dimes than quarters

 

Replace D with Q + 2 in top equation

 

Q + Q + 2 = 18

2Q = 16

Q = 8

 

There are 8 quarters.

 

This means there are 10 dimes and the total is indeed $3.00

Answer 2

Hi Brandy,

 

Let's begin by assigning the letter x to represent our unknown (number of quarters).  Since there are two more dimes than quarters, we can represent the number of dimes as x + 2.

 

Now we can write an equation (using our expressions for the numbers of quarters and dimes) to express their sum as 3.00 and use it to solve for x (number of quarters):

    (0.25)(x) + (0.10)(x + 2) = 3.00

    0.25x + 0.10x + 0.20 = 3.00

    0.35x + 0.20 = 3.00

    0.35x = 3.00 - 0.20

    0.35x = 2.80

          x = 2.80/0.35

          x = 8 (number of quarters)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.