Jun Wei has 12 more 10 cent coins than 20 cent coins. The total value of all his coins is $5.40. Find the total number of coins he has.
Jun Wei has 12 more 10 cent coins than 20 cent coins. The total value of all his coins is $5.40. Find the total number of coins he has.
To find the total number of coins Jun Wei has, let's break down the problem step by step.
Let's assume Jun Wei has "x" number of 10 cent coins and "y" number of 20 cent coins.
According to the problem, Jun Wei has 12 more 10 cent coins than 20 cent coins. So, we can write the equation:
x = y + 12 ----(1)
Next, we need to consider the total value of all his coins. The value of one 10 cent coin is $0.10, and the value of one 20 cent coin is $0.20. So, we can write the equation for the total value as:
0.10x + 0.20y = 5.40 ----(2)
Now, we have a system of two equations (equation 1 and equation 2) that we can solve to find the values of "x" and "y".
To solve the system of equations, we can use the substitution or elimination method. Let's use the substitution method here:
From equation (1), we know that x = y + 12. We can substitute this value of x in equation (2).
0.10(y + 12) + 0.20y = 5.40
0.10y + 1.20 + 0.20y = 5.40
0.30y + 1.20 = 5.40
0.30y = 5.40 - 1.20
0.30y = 4.20
Divide both sides by 0.30:
y = 4.20 / 0.30
y = 14
Now that we know the value of y, we can substitute it back into equation (1) to find the value of x:
x = y + 12
x = 14 + 12
x = 26
Therefore, Jun Wei has 26 10 cent coins and 14 20 cent coins, making a total of 26 + 14 = 40 coins.