Question

I have 38 coins in my hand. Some coins are worth one dollar some coins are worth two dollars. The total worth of the coins is 54 dollars. How many coins of each denomination do I have?

Answer 1

The answer is

• Number of one dollar coins = 22.
• Number of two dollar coins = 16.

Step-by-step explanation:

Total number of coins = 38

let number of one dollar coins be a

number of two dollar coins be b

Then,

a + b = 38

a = 38 - b .......(equation 1)

Also The total worth of the coins is 54 dollars.

a + 2b = 54 ......(equation 2)

Put equation 1 in equation 2 ,

a + 2b = 54

38 - b + 2b = 54

Move all terms containing b to the Left hand side of the equation.

-b + 2b = 54 - 38

b = 16

Now put value of b in equation 1.

a = 38 - b

a = 38 - 16

a = 22

Hence,

• Number of one dollar coins is 22.
• Number of two dollar coins is 16.

Answer 2

• 22 one-dollar coins and 16 two-dollar coins

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Let the number of one-dollar coins be x and two-dollar coins be y.

Number of coins is 38:

• x + y = 38

Total worth of the coins is 54 dollars:

• x + 2y = 54

We have a system of equations. Solve it by elimination, subtract the equations side-by-side:

• x + 2y - x - y = 54 - 38
• y = 16

Find the value of x by substituting 16 for y:

• x + 16 = 38
• x = 22