David took out all his coins in his piggy bank. They were made up of only fifty cents and twenty cents coin. There are 12 fifty cents coins more than twenty cents coin. The total value of fifty cents coin is 21$ more than the total value of twenty cents coin . Find the number of fifty cents coin
60cent coins
Can you please give step by step explaination
number of twenty-cent coins --- x
number of fifty-cent coins ----- x+12
value of x+12 fifty-cent coins = 50(x+12)
value of x twenty-cent coins = 20x
50(x+12) - 20x = 2100
50x + 600 - 20x = 2100
30x = 1500
x = 50
There are 50 twenty-cent coins
and 62 fifty cent coins
check:
value of 62 fifty-cent coins = 31
value of 50 twenty-cent coins = 10
which is a difference of 21$
To find the number of fifty cents coins, let's assign variables to the unknown values.
Let's say the number of fifty cents coins is 'x', and the number of twenty cents coins is 'y'.
Given that there are 12 fifty cents coins more than twenty cents coins, we can represent this as:
x = y + 12
Now, we need to consider the total value of the coins. The value of each fifty cents coin is $0.50, and the value of each twenty cents coin is $0.20.
The total value of the fifty cents coins can be represented as 0.50*x, and the total value of the twenty cents coins can be represented as 0.20*y.
Given that the total value of the fifty cents coins is $21 more than the total value of the twenty cents coins, we can set up the following equation:
0.50*x = 0.20*y + 21
Now we have two equations:
x = y + 12
0.50*x = 0.20*y + 21
To solve these equations, we can use the substitution method.
First, substitute the value of 'x' from the first equation into the second equation:
0.50*(y + 12) = 0.20*y + 21
Next, distribute 0.50 to y and 12:
0.50 * y + 0.50 * 12 = 0.20 * y + 21
0.50y + 6 = 0.20y + 21
Now, subtract 0.20y from both sides to isolate the variables:
0.50y - 0.20y + 6 = 21
0.30y + 6 = 21
Next, subtract 6 from both sides:
0.30y = 15
Divide both sides by 0.30 to solve for 'y':
y = 15 / 0.30
y = 50
Now that we have found the value of 'y' (number of twenty cents coins), we can substitute this value back into the first equation to solve for 'x':
x = y + 12
x = 50 + 12
x = 62
Therefore, there are 62 fifty cents coins in the piggy bank.