You have twice as many 20 cent coins as 10 cents coins and half the number of 5 cent coins as 10 cent coins. If you have R4,20 altogether, find out how many of each coin denomination do you have?
Let's solve this problem step-by-step.
Step 1: Assign variables.
Let's assign variables to each type of coin.
Let:
x = the number of 10 cent coins
2x = the number of 20 cent coins (twice the number of 10 cent coins)
0.5x = the number of 5 cent coins (half the number of 10 cent coins)
Step 2: Calculate the value of each coin type.
The value of 10 cent coins is 10x cents.
The value of 20 cent coins is 20(2x) = 40x cents.
The value of 5 cent coins is 5(0.5x) = 2.5x cents.
Step 3: Write an equation for the total value of the coins.
The total value of the coins is R4,20, which is equal to 420 cents.
So, we can write the equation:
10x + 40x + 2.5x = 420
Step 4: Solve the equation.
Combining like terms, we have:
52.5x = 420
Solving for x, we divide both sides of the equation by 52.5:
x = 8
Step 5: Calculate the number of each coin.
Now that we know x = 8, we can substitute it back into our expressions for each coin type.
The number of 10 cent coins (x) = 8 coins
The number of 20 cent coins (2x) = 2 * 8 = 16 coins
The number of 5 cent coins (0.5x) = 0.5 * 8 = 4 coins
Therefore, you have 8 ten cent coins, 16 twenty cent coins, and 4 five cent coins.
To solve this problem, we can set up a system of equations based on the given information. Let's denote the number of 10 cent coins as x.
Given that you have twice as many 20 cent coins as 10 cent coins, we can represent the number of 20 cent coins as 2x.
Also, given that the number of 5 cent coins is half the number of 10 cent coins, we can represent the number of 5 cent coins as 0.5x.
Now, let's calculate the total value of the coins:
The value of the 10 cent coins is 10 * x cents.
The value of the 20 cent coins is 20 * 2x cents.
The value of the 5 cent coins is 5 * 0.5x cents.
Since the total value of the coins is R4.20, we can write the equation:
10x + 20 * 2x + 5 * 0.5x = 420 cents.
Simplifying the equation, we have:
10x + 40x + 2.5x = 420.
52.5x = 420.
Dividing both sides by 52.5, we find:
x ≈ 8.
Therefore, the number of 10 cent coins is approximately 8.
The number of 20 cent coins is 2 * 8 = 16.
The number of 5 cent coins is 0.5 * 8 = 4.
So, you have 8 10 cent coins, 16 20 cent coins, and 4 5 cent coins.
suppose you have x,y,z of 5¢, 10¢, 20¢ coins, respectively. Then you know that
z = 2y
y = 2x
5x+10y+20z = 420
Now just solve as usual