Math problem, calculation quiz - what's the most cost-efficient solution?

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55x42
55x42
18x42
51x96

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Are those numbers in feet or inches? Kind of a crutial detail....

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Just ask ChatGPT

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Thanks! Let's work through the most cost-effective way to cover the four walls, accounting for **waste** and aiming to **minimize total cost**.

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### ?? Wall Sizes

Total square footage to cover:

1. 55" × 42" = 2,310 in² (x2 walls) ? 4,620 in²
2. 18" × 42" = 756 in²
3. 51" × 96" = 4,896 in²

**Total = 10,272 in²** = **71.33 ft²**

Let's round up slightly and assume **at least 75 ft²** to include some **waste (5%–10%)**.

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### ?? Board Sizes and Prices

| Size (inches) | Area (in²) | Price | Cost per in² |
| ------------- | ---------- | ----- | ------------ |
| 96" × 148" | 14,208 | \$108 | **\$0.0076** |
| 24" × 96" | 2,304 | \$91 | \$0.0395 |
| 32" × 48" | 1,536 | \$40 | \$0.0260 |

?? **Observation**:
The **96"×148"** board is **by far** the **cheapest per square inch**, even if it's large and potentially harder to work with.

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### ?? Strategy: Use the Large Board First

We want to use as **few large boards** as possible to minimize cost, and only use the smaller ones when necessary (for smaller or odd pieces).

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### Step-by-Step Fit Plan

Let’s see if one 96"x148" board (14,208 in²) can cover most of the space:

* Total area needed: 10,272 in²
* One large board = 14,208 in² ? **more than enough** in raw area.
* But now we need to verify **actual fitting**.

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### ? Try to Fit All Walls from One 96"x148" Sheet

We’ll check if we can lay out the four wall panels **within** one sheet.

#### Wall Cut Plan from 96"x148":

* 2x 55"x42"
* 1x 18"x42"
* 1x 51"x96"

Try stacking horizontally or vertically.

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#### Option A: Layout on 96" Height (tall side up), 148" width:

\| Width used: |

* 55" + 55" = 110"
* 18" = fits in remaining 38"
? All three smaller walls fit in one row across the top (42" tall), with width 128" used, still under 148".

Then, the big wall (51"x96") goes underneath — 96" height fits, 51" width easily fits under 148".

? **All pieces fit in one 96"x148" board.**

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### ? Best Option: Buy **1 Large Sheet** (96"x148")

* Cost: **\$108**
* Covers: All four wall areas, with extra leftover
* Cheapest per square inch
* Efficient fit with minimal cutting

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### ? Optional Waste Buffer

If you're concerned about mistakes or cutting waste:

* Add **1 small extra board**: 32"x48" ? \$40
(adds 1,536 in² = 10.67 ft²)

Still total cost = **\$148**

But if you're confident in the cuts, you can stick with just **1 large sheet**.

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### ? Final Recommendation:

| Board Type | Quantity | Cost |
| --------------------- | ---------------- | --------------- |
| 96"x148" | 1 | \$108 |
| **Optional:** 32"x48" | 1 (extra buffer) | \$40 |
| **Total** | 1 or 2 boards | **\$108–\$148** |

Let me know if you’d like me to diagram the layout on the board!

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