A sports magazine prints 12
 issues per year, and a technology magazine prints 10
 issues per year. The total number of pages in all the issues of the sports magazine for one year is 32
 more than the total number of pages in all the issues of the technology magazine for one year. Each issue of the sports magazine has 18
 fewer pages than each issue of the technology magazine.

The system of equations shown can be used to determine s
, the number of pages in each issue of the sports magazine, and t
, the number of pages in each issue of the technology magazine.
 
s = t−18
12s = 10t+32

How many pages are in the technology magazine?
A.142
 pages
B.106
 pages
C.124
 pages
D.88
 pages

We are given two equations that model the relationship between the number of pages in the sports magazine and the technology magazine:

1. \( s = t - 18 \) — each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine.
2. \( 12s = 10t + 32 \) — the total number of pages in all issues of the sports magazine is 32 more than the total number of pages in all issues of the technology magazine over a year.

We need to solve this system of equations for \( t \), the number of pages in each issue of the technology magazine.

### Step 1: Substitute the first equation into the second equation
From the first equation, we know \( s = t - 18 \). Substitute this into the second equation:

\[
12(t - 18) = 10t + 32
\]

### Step 2: Expand and simplify the equation
Distribute the 12 on the left-hand side:

\[
12t - 216 = 10t + 32
\]

### Step 3: Move all terms involving \( t \) to one side
Subtract \( 10t \) from both sides:

\[
2t - 216 = 32
\]

### Step 4: Solve for \( t \)
Add 216 to both sides:

\[
2t = 248
\]

Divide both sides by 2:

\[
t = 124
\]

Thus, each issue of the technology magazine has **124 pages**.

### Answer:
**C. 124 pages**

Would you like more details or have any questions?

Here are some related questions to consider:
1. What is the number of pages in each issue of the sports magazine?
2. How many total pages does the sports magazine have over a year?
3. How many total pages does the technology magazine have over a year?
4. How would the system of equations change if the sports magazine had 25 fewer pages per issue?
5. How can we represent the relationship between the two magazines graphically?

**Tip:** When solving systems of equations, always look for substitution opportunities to simplify the process.

A sports magazine prints 12 issues per year, and a technology magazine prints 10 issues per year. The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. Each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine.

The system of equations shown can be used to determine s, the number of pages in each issue of the sports magazine, and t, the number of pages in each issue of the technology magazine.

s = t−18
12s = 10t+32

How many pages are in the technology magazine?

A. 142 pages
B. 106 pages
C. 124 pages
D. 88 pages

Learn how to solve a system of equations involving the number of pages in sports and technology magazines. This problem covers algebraic concepts such as substitution and linear equations, with a step-by-step solution. Suitable for students in Grades 7-9.

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