A store warehouses 40 more portables than big-screen TV sets, and 14 more consoles than big-screen sets. Storage costs for portable TV sets are $1.50 a month, console TV sets are $4.00 a month, and Big-screen sets are $7.50 a month. If storage costs are $298 per month, how many big-screen sets are in stock?

Let:

- $ x $ represent the number of big-screen TV sets.
- $ x + 40 $ represent the number of portable TV sets (since the store has 40 more portable sets than big-screen sets).
- $ x + 14 $ represent the number of console TV sets (since the store has 14 more console sets than big-screen sets).

Now, using the given monthly storage costs:

- The storage cost for portable TV sets is $ 1.50 $ dollars per month, so the total cost for portables is $ 1.50(x + 40) $.
- The storage cost for console TV sets is $ 4.00 $ dollars per month, so the total cost for consoles is $ 4(x + 14) $.
- The storage cost for big-screen TV sets is $ 7.50 $ dollars per month, so the total cost for big-screen sets is $ 7.50x $.

The total storage cost is $298 per month, so we can set up the following equation:

\[
1.50(x + 40) + 4(x + 14) + 7.50x = 298
\]

Now, let's solve for $ x $:

\[
1.50(x + 40) = 1.50x + 60
\]
\[
4(x + 14) = 4x + 56
\]
Substitute these into the equation:

\[
(1.50x + 60) + (4x + 56) + 7.50x = 298
\]

Combine like terms:

\[
1.50x + 4x + 7.50x + 60 + 56 = 298
\]
\[
13x + 116 = 298
\]

Subtract 116 from both sides:

\[
13x = 182
\]

Now, divide by 13:

\[
x = \frac{182}{13} = 14
\]

So, there are **14 big-screen TV sets** in stock.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How many portable TV sets are in stock?
2. How many console TV sets are in stock?
3. What is the total cost of storing just the portable TV sets?
4. What is the total cost of storing just the console TV sets?
5. If the cost of storing big-screen TVs increased to $9.00 per set, how would the total storage cost change?

**Tip:** When setting up equations, carefully define variables based on the problem's relationships.

Solve the algebraic problem where a store warehouses 40 more portables and 14 more consoles than big-screen TV sets, with storage costs of $298 per month. Learn how to use linear equations to determine the number of big-screen sets in stock. Suitable for students in Grades 8-10.

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