Question

Dave Bowers collects U.S. gold coins. He has a collection of 36 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $540, how many of each denomination does he have?please help me

Answer 1

Given

Total coins = 36

face value of the coins is ​$​540

Some are $10 coins and rest are $20coins.

Find

Number of each denomination he have.

Step-by-step explanation

Let number of $10 coins = x

Number of $20 coins = y

according to the question

x + y = 36

10x + 20y = 540

soving these equation ,

`\begin{gathered} x+y=36 \\ 10(x+2y)=540\Rightarrow x+2y=54 \end{gathered}`

subtract both equations,

`\begin{gathered} x+y-x-2y=36-54 \\ -y=-18 \\ y=18 \end{gathered}`

put value of y in any one equation to find the value of x ..

x+18=36

x= 18

Final Answer

Therefore , the number of $10 coins = 18 and number of $20 coins = 18