A bag contains forty coins, all of them either 2c or 5c coins. Let there be x 2c coins and y 5c coins. If the value of money in the bag is $1.55, find the number of each kind.
5x = 2y therefore
x = 2/5y
x + y = 155
Substitute 2/5y for x in last equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the last equation.
To solve this problem, we can set up a system of equations based on the information given.
Let's assume that there are x 2c coins and y 5c coins in the bag.
The first equation is based on the number of coins:
x + y = 40 (since there are 40 coins in total)
The second equation is based on the value of the money in the bag:
0.02x + 0.05y = 1.55 (since each 2c coin is worth $0.02 and each 5c coin is worth $0.05)
Now we can solve this system of equations. There are several methods we can use, such as substitution or elimination. Let's use the elimination method:
Multiplying the first equation by 0.02, we get:
0.02(x + y) = 0.02(40)
0.02x + 0.02y = 0.8
Now we can subtract this equation from the second equation:
(0.02x + 0.05y) - (0.02x + 0.02y) = 1.55 - 0.8
Simplifying the equation, we get:
0.05y - 0.02y = 0.75
0.03y = 0.75
y = 0.75 / 0.03
y ≈ 25
Substitute this value back into the first equation to find x:
x + 25 = 40
x = 40 - 25
x = 15
So, there are 15 coins worth 2c and 25 coins worth 5c in the bag.