Xuan Yun has a total of 24 coins in her piggy bank. Some of them are twenty-cent coins and the others are fifty-cent coins. Thetotal savings is $6.90. How many twenty-cent and fifty-cent coins does she have?
number of 25 cent coins --- x
number of 50 cent coins ---- 24-x
25x + 50(24-x) = 690
solve for x and back-substitute
To solve this problem, we can use algebraic equations. Let's represent the number of twenty-cent coins as "x" and the number of fifty-cent coins as "y".
From the problem, we know the following information:
1) Xuan Yun has a total of 24 coins in her piggy bank. So we can write the equation: x + y = 24.
2) The total savings in her piggy bank is $6.90. Since each twenty-cent coin is worth $0.20 and each fifty-cent coin is worth $0.50, we can write the equation: 0.20x + 0.50y = 6.90.
Now we have a system of equations. We can solve this system of equations simultaneously to find the values of x and y.
First, let's solve the first equation for x. Subtract y from both sides of the equation:
x = 24 - y
Now substitute this expression for x in the second equation:
0.20(24 - y) + 0.50y = 6.90
Distribute the 0.20:
4.80 - 0.20y + 0.50y = 6.90
Combine like terms:
0.30y = 2.10
Divide both sides by 0.30:
y = 7
Now substitute the value of y back into the first equation to find x:
x + 7 = 24
Subtract 7 from both sides:
x = 17
Therefore, Xuan Yun has 17 twenty-cent coins and 7 fifty-cent coins in her piggy bank.