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Dave Bowers collects U.S. gold coins. He has a collection of 43 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $640. how many of each denomination does he have?

User Leyton
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1 Answer

3 votes

Answer:

There are 22 $10 coins and 21 $20 coins.

Explanation:

Let x = the number of $10 coins

Let y = the number of $20 coins

You have two unknows so you need two equations.

x + y = 43

10x + 20y = 640.

Rewrite the first equation solving for x

x + y = 43

x = 43 - y Substitute 43 - y in for x in the second equation.

10x + 20 y = 640

10(43 - y) + 20y = 640

430 - 10y + 20y = 640 Subtract 430 from both sides of the equation

-10y + 20y = 210 Combine the y's

10y = 210 Divide both sides by 10

y = 21 This is the number of $20 coins.

Substitute 21 in for y in either of the original equations to solve for x

x + 21 = 43 Subtract 21 from both sides

x = 22 This is the number of $10 coin.

Check:

Substitute in 21 for y and 22 for x

x + y = 43

21 + 22 = 43

43 = 43 checks

10x + 20y = 640

10(22) + 20(21) = 640

220 + 420 = 640

640 = 640 Checks

User Emmalyn
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