The letter n confuses everyone at first. It is not magic. It is just a blank we gave a name. Click Next.
You save $3 every day. Same amount, every single day.
money = 3 × day number
Day 1: 3×1=3 ✓ Day 2: 3×2=6 ✓ Day 3: 3×3=9 ✓ — one rule works for EVERY day. But "day number" is long to write…
money = 3 × n
We got tired of writing "day number". So we gave the blank a short name: n. That is ALL n is — a short name for the blank.
Three small writing rules.
Rule 1 — the times sign hides.
3 × n is written 3n (a number glued to a letter always means MULTIPLY)
Rule 2 — n is a fill-in box. Pick a day, drop it in the box:
n = 4: 3n = 3 × 4 = $12
n = 10: 3 × 10 = $30 n = 100: 3 × 100 = $300
Rule 3 — a plus or minus next to n means WALK along the days.
Today is day n. Tomorrow is n + 1. Yesterday was n − 1.
n is today. n + 2 = walk 2 days forward. n − 2 = walk 2 days back. If n = 7: n+2 = 9 and n−2 = 5.
Same idea, new name for the blank.
In the tile lessons, the blank is the design number:
Design 1, Design 2, Design 3 … Design n
tiles = 3n + 1 → "3 times the design number, plus the starter."
n goes IN. The answer comes OUT.
n = 5 → [ 3 × 5 + 1 ] → 16 tiles
n is the QUESTION ("which design?"). It is never the answer.
3n is NOT "three-something". If n = 4, then 3n = 3 × 4 = 12 — not 34! A number glued to a letter always means multiply.
Second trap: n is not the answer. n is which day, which design, which one. The answer is what the rule gives you AFTER you fill n in.
n is a blank box with a name. Fill it in, multiply, done.
In the rule tiles = 4n + 1, what does n stand for?
Answer: (B) The design number.
n is the blank where you put WHICH design you want. Then the rule gives the tiles.
Quick check: Design 2 → 4 × 2 + 1 = 9 tiles. n was 2. The answer was 9. They are different jobs!