Question

Mylee is a stamp collector and buys commemorative stamps. Suppose she buys a combination of 47-cent stamps and 34-cent stamps at the post office. If she spends exactly $21.55 on 50 stamps, how many of each type did she buy?

Answer 1

Mylee bought approximately 35 stamps with a value of 47 cents each and 15 stamps with a value of 34 cents each.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let's define x as the number of 47-cent stamps Mylee buys and y as the number of 34-cent stamps she buys. We can set up the following equations:

x + y = 50 (equation 1)

0.47x + 0.34y = 21.55 (equation 2)

First, we can solve equation 1 for x and substitute it into equation 2:

y = 50 - x

0.47x + 0.34(50 - x) = 21.55

Simplifying and solving for x:

0.47x + 17 - 0.34x = 21.55

0.13x = 4.55

x = 4.55 / 0.13

x ≈ 35

So Mylee bought approximately 35 stamps with a value of 47 cents each.

We can substitute this value back into equation 1 to find the number of 34-cent stamps:

35 + y = 50

y = 15

Mylee bought approximately 35 stamps with a value of 47 cents each and 15 stamps with a value of 34 cents each.

Answer 2

Let x represent the number of 47-cent stamps that Mylee bought, and y the number of 34-cent stamps. Using the given information you can set the following system of equations:

`\begin{gathered} 0.47x+0.34y=21.55, \\ x+y=50. \end{gathered}`

Multiplying the second equation by 0.47 and subtracting it from the first equation, you get:

`0.47x-0.47x+0.34y-0.47y=21.55-23.5.`

Solving the above equation for y, you get:

`\begin{gathered} -0.13y=-1.95, \\ y=(1.95)/(0.13), \\ y=15. \end{gathered}`

Using the second equation of the system you get:

`\begin{gathered} x+15=50, \\ x=50-15, \\ x=35. \end{gathered}`

Answer:

`\begin{gathered} 35\text{ of 47-cent stamps,} \\ 15\text{ of 34-cent stamps.} \end{gathered}`