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?

Answer:The number of dimes = 32The number of quarters  = 14Step-by-step explanation:Here, the total number of coins combined = 46Let us assume the number of dimes = mSo, the Number of quarter = Total Coins - Number of dimes  = 46 - mNow,as we know:1 dime = $0.1So, m dimes  = m x ($0.1) = $(0.1 m)1 Quarter  = $0.25So, ( 46 - m ) Quarters  = (46 - m ) x ( $ 0.25)   = 11.5 - 0.25 mAlso, 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 = - 4.8or, m = 4.8/0.15  =  32⇒ m = 32Hence, the number of dimes = m = 32And the number of quarters  = 46 - m= 46 -32 = 14