Dave Bowers collects U. S. gold coins. He has a collection of 41 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $590, how many of each denomination does he have?Dave Bowers collects U. S. gold coins. He has a collection of 34 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $500, how many of each denomination does he have?

1. He has 23 coins in $10, and 18 coins in $20

2. He has 18 coins in $10, and 16 coins in $20

Explanation:

The number of $10 and $20 are two variables that can only be determined simultaneously. The product of the number of each type of coin with the value of each coin gives the total amount owned.

Let the number of  of $10 coins owned be x and that of $20 be y

If he has a collection of 41 coins then

x + y = 41

If the face value of the coins is $590

then,

10x + 20y = 590

solving both simultaneously

x + y = 41

x + 2y = 59

y = 59 - 41

= 18

x = 41- 18

= 23

It means he has 23 coins in $10, and 18 coins in $20.

If he has a collection of 34 coins then

x + y = 34

If the face value of the coins is $500

then,

10x + 20y = 500

solving both simultaneously

x + y = 34

x + 2y = 50

y = 50 - 34

= 16

x = 34- 16

= 18

It means he has 18 coins in $10, and 16 coins in $20

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