Suppose you have a coin collection of dimes and quarters containing 46 coins. If you have 6.70 dollars, how many of each type of coin do you have?

The number of dimes = 32

The number of quarters = 14

Step-by-step explanation:

Here, the total number of coins combined = 46

Let us assume the number of dimes = m

So, the Number of quarter = Total Coins - Number of dimes = 46 - m

Now, as we know:

1 dime = $0.1

So, m dimes = m x ($0.1) = $ (0.1 m)

1 Quarter = $0.25

So, (46 - m) Quarters = (46 - m) x ($ 0.25) = 11.5 - 0.25 m

Also, given the total amount of coins = $ 6.70

⇒ Value of (Dimes + Quarters) = $ 6.70

or, (0.1 m) + 11.5 - 0.25 m = 6.70

-0.15 m = - 4.8

or, m = 4.8/0.15 = 32

⇒ m = 32

Hence, the number of dimes = m = 32

And the number of quarters = 46 - m = 46 - 32 = 14