Box A contained only 50 cent coins while Box B contained only 20 cents coins, Box B has 60 more coins than Box A but the value of all the coins in Box A is $4.50 more than the value of all the coins in Box B. Find the amount of money in Box A.
Please help me to solve this question, thanks so much.
number of coins in box B ---- b , 20 cent pieces
number of coins in box A ---- a , 50 cent pieces
equation dealing with number of coins:
b = a+60
equation dealing with value of coins:
50a - 20b = 450
5a - 2b = 45
use substitution:
5a - 2(a+60) = 45
5a - 2a - 120 = 45
3a = 165
a = 55 , then b = 115
check:
Box A contains 55(50) = $27.50
box B contains 20(115) = $23.00
box A contains 27.50 - 23.00 more , or $4.50
(my answer is correct)
Let's first assume the number of coins in Box A as "a" and the number of coins in Box B as "b".
According to the problem, we know that Box B has 60 more coins than Box A. This can be expressed as:
b = a + 60 (Equation 1)
We are also given that the value of all the coins in Box A is $4.50 more than the value of all the coins in Box B. We need to determine the value of the coins in each box.
Let's assume that each 50 cent coin is worth $0.50 and each 20 cent coin is worth $0.20.
So, the value of all the coins in Box A can be expressed as:
0.50a (Equation 2)
Similarly, the value of all the coins in Box B can be expressed as:
0.20b (Equation 3)
According to the problem, the value of all the coins in Box A is $4.50 more than the value of all the coins in Box B. This can be expressed as:
0.50a = 0.20b + 4.50
Now, let's substitute the value of "b" from Equation 1 into Equation 4:
0.50a = 0.20(a + 60) + 4.50
Simplifying the equation:
0.50a = 0.20a + 12 + 4.50
0.50a - 0.20a = 16.50
0.30a = 16.50
Dividing both sides of the equation by 0.30:
a = 55
Therefore, there are 55 coins in Box A.
To solve this problem, we can set up a system of equations.
Let's denote the number of coins in Box A as "x" and the number of coins in Box B as "y".
Given that Box B has 60 more coins than Box A, we can write:
y = x + 60. ---- Equation 1
Given that the value of all the coins in Box A is $4.50 more than the value of all the coins in Box B, we need to consider the value of the coins as well.
The value of a single 50 cent coin is $0.50, so the value of all the coins in Box A is 0.50x.
The value of a single 20 cent coin is $0.20, so the value of all the coins in Box B is 0.20y.
Given that the value of all the coins in Box A is $4.50 more than the value of all the coins in Box B, we can write:
0.50x = 0.20y + 4.50. ---- Equation 2
Now we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system to find the value of x, which represents the amount of money in Box A.
To solve the system, we can substitute the value of y from Equation 1 into Equation 2:
0.50x = 0.20(x + 60) + 4.50.
Let's simplify and solve this equation:
0.50x = 0.20x + 12 + 4.50
0.50x - 0.20x = 12 + 4.50
0.30x = 16.50
x = 16.50 / 0.30
x ≈ 55
Therefore, the amount of money in Box A is approximately $55.