Question

A man went to a post office to buy some stamps. If he bought x, 50 cents stamps and y, 25 cents stamps, the total cost would have been $3.50. If, however, he bought twice as many 50 cents stamps and half as many 25 cents stamps, then the total cost would have been $4.75. Evaluate x and y.​

Answer 1

We can start by setting up two equations based on the given information:

Equation 1: 0.5x + 0.25y = 3.5
Equation 2: 1x + 0.125y = 4.75

To solve for x and y, we need to eliminate one of the variables. We can do this by multiplying Equation 1 by 2 and subtracting it from Equation 2:

2(0.5x + 0.25y) = 2(3.5)
=> x + 0.5y = 7

1x + 0.125y = 4.75
- (x + 0.5y = 7)
------------------------
-0.375y = -2.25
=> y = 6

Now we can substitute y = 6 into either Equation 1 or 2 to solve for x:

0.5x + 0.25y = 3.5
0.5x + 0.25(6) = 3.5
0.5x + 1.5 = 3.5
0.5x = 2
=> x = 4