A business executive bought 40 stamps for $13.68. The purchase included 37 cents stamps and 23 cents stamps. How many of each type of stamp were bought?
x + y = 40 (number of stamps)
23 x + 37 y = 1368 (number of cents)
Solve for x and y
23 (40 -y) + 37 y = 1368
Now you only have to solve for y
Let's assume the executive bought x number of 37 cents stamps and y number of 23 cents stamps.
According to the given information, the total number of stamps bought is 40, so we can write the equation:
x + y = 40 (Equation 1)
Now let's calculate the total cost of the stamps:
The cost of the 37 cents stamps would be 37x cents.
The cost of the 23 cents stamps would be 23y cents.
The total cost of the stamps is $13.68, which is equal to 1368 cents.
Therefore, we can write the equation:
37x + 23y = 1368 (Equation 2)
We have two equations (Equation 1 and Equation 2) that need to be solved simultaneously to find the values of x and y.
To solve these equations, we can use the substitution method or elimination method.
Let's use the elimination method:
Multiplying Equation 1 by 37, we get:
37x + 37y = 1480 (Equation 3)
Now, subtracting Equation 2 from Equation 3, we get:
37x + 37y - 37x - 23y = 1480 - 1368
14y = 112
Dividing both sides of the equation by 14, we get:
y = 8
Now, substituting the value of y into Equation 1, we can find the value of x:
x + 8 = 40
x = 32
Therefore, the executive bought 32 stamps of 37 cents each and 8 stamps of 23 cents each.
To find out how many of each type of stamp were bought, we need to set up a system of equations based on the given information.
Let's assume the number of 37 cents stamps bought is x, and the number of 23 cents stamps bought is y.
From the given information, we have two pieces of information:
1. The executive bought a total of 40 stamps: x + y = 40
2. The total cost of the stamps was $13.68: (37 cents value stamps * x) + (23 cents value stamps * y) = $13.68
Now, we can solve this system of equations to find the values of x and y.
First, we will solve equation 1 for x:
x = 40 - y
Next, substitute the value of x in equation 2:
(37 * (40 - y)) + (23 * y) = 13.68
Expanding this equation gives:
1480 - 37y + 23y = 13.68
Combine like terms:
1480 - 14y = 13.68
Subtract 1480 from both sides:
-14y = -1466.32
Divide both sides by -14:
y = 104.74
Since we can't have a fraction of a stamp, we know this is incorrect.
Let's re-evaluate our calculations:
We just realized that our value for y cannot be a fraction, as the y variable represents the number of 23 cents stamps. So, let's either try a different approach or adjust our assumptions.
Since 13.68 is divisible by 0.23 (the value of the 23 cents stamp), we can see that the number of 23 cents stamps should be a whole number.
Let's find the integer solutions for y and then find x using equation 1.
Using trial and error, we find that when y = 32, the equation yields a whole number for x:
x = 40 - y = 40 - 32 = 8
Therefore, the executive bought 8 stamps with a value of 37 cents each and 32 stamps with a value of 23 cents each.