Question

Dave bowers collects u.s. gold coins. He has a collection of 46 coins. Some are $10, the rest are $20 coins. If the face value of the coins is $700, how many of each denomination does he have?

Answer 1

Using a system of two equations, we can determine that Dave Bowers has 22 $10 coins and 24 $20 coins in his collection of 46 coins.

Step-by-step explanation:

Dave Bowers collects U.S. gold coins and has 46 in total. To determine how many of each denomination he has, we can set up two equations based on the number of coins and their total face value. Let "x" represent the number of $10 coins and "y" the number of $20 coins. We have two equations:

1. x + y = 46 (the total number of coins)
2. 10x + 20y = 700 (the total face value of the coins)

We can solve this system of equations by substituting from the first equation into the second. From the first equation, we get y = 46 - x. Substituting this into the second equation:

10x + 20(46 - x) = 700

10x + 920 - 20x = 700

-10x + 920 = 700

-10x = 700 - 920

-10x = -220

x = 22

Therefore, Dave has 22 $10 coins, and since y = 46 - x, y = 46 - 22, which means he has 24 $20 coins.