Question

Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.

This system of equations models the given information for both stamp types.

x – y = 34

x + y = 212

Solve the system of equations.

How many foreign stamps does Malik have?

foreign stamps



How many domestic stamps does Malik have?

domestic stamps

Answer 1

We are given the following system of equations:

1. \( x - y = 34 \) (where \( x \) is the number of domestic stamps and \( y \) is the number of foreign stamps)
2. \( x + y = 212 \)

We can solve this system using the substitution or elimination method. Let's use the substitution method:

From equation (1), we can express \( x \) in terms of \( y \):

\[
x = y + 34
\]

Now, we can substitute \( x \) in equation (2):

\[
(y + 34) + y = 212
\]

Combining like terms gives:

\[
2y + 34 = 212
\]

Next, we subtract 34 from both sides:

\[
2y = 178
\]

Now, divide by 2:

\[
y = 89
\]

Now that we have the number of foreign stamps (\( y \)), we can substitute \( y \) back into the equation for \( x \):

\[
x = y + 34 = 89 + 34 = 123
\]

So, Malik has:

- **Foreign stamps:** \( y = 89 \)
- **Domestic stamps:** \( x = 123 \)

To summarize:
- Malik has **89 foreign stamps.**
- Malik has **123 domestic stamps.**