A man went to a post office to buy stamps. He bought x, 50 cent stamps and y, 25 cent stamps for $3.50. If he bought twice as many 50 cent stamps and half as many 25 cent stamps, the cost would be $4.75. Evaluate x and y
total cost for x,y
50x + 25y = 350
total cost for new x,y
50(2x) + 25(y/2) = 475
Putting it together:
50x + 25y = 350
100x + 25/2 y = 475
or, with no ugly fractions
50x + 25y = 350
200x + 25y = 950
Subtract top from bottom
150x = 600
x = 4
y = 6
50(4) + 25(6) = 350
50(8) + 25(3) = 475
To solve this problem, we can set up a system of equations based on the given information.
Let's start by defining the variables:
x = number of 50 cent stamps
y = number of 25 cent stamps
From the first statement, we can create an equation for the total cost:
0.50x + 0.25y = 3.50 -- Equation 1
Now, let's consider the second statement. It states that if the man bought twice as many 50 cent stamps and half as many 25 cent stamps, the cost would be $4.75. We can express this as:
0.50(2x) + 0.25(0.5y) = 4.75
Simplifying this equation:
x + 0.125y = 4.75 -- Equation 2
Now, we have a system of two equations with two variables. To find the values of x and y that satisfy the system, we can solve the equations simultaneously.
We can multiply Equation 1 by 4 to eliminate decimals:
2x + y = 14 -- Equation 3
Now, we can multiply Equation 2 by 8 to eliminate decimals:
8x + y = 38 -- Equation 4
To solve the system, we can subtract Equation 3 from Equation 4:
(8x + y) - (2x + y) = 38 - 14
6x = 24
Dividing both sides of the equation by 6, we get:
x = 4
Substituting this value back into Equation 3, we can find y:
2(4) + y = 14
8 + y = 14
y = 14 - 8
y = 6
Therefore, x = 4 and y = 6. The man bought 4, 50 cent stamps and 6, 25 cent stamps.