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A merchant counts goods the same amount three different ways. The same quantity can be written as a percentage, a decimal, or a fraction — and they're all the same thing.
The bar below has 100 cells. Some are shaded gold. Look at the shading, then tell me the three names for what's shaded.
"What is X% of Y?" is asking for a portion of a total — a tax on a price, a tip on a bill, a discount off a tag.
Some of these are so familiar you'll know them by heart. Find the portions below; then we'll name the rule.
The merchant spent 40c out of every $2 on salt. What percent is that?
The bar below has 100 cells — each cell is 1% of the whole. Count how many cells the part occupies, then you'll have your percent directly.
The merchant buys cheese for $50 and sells at a 20% markup. Find the new price.
Work it out the long way first: find 20% of $50, then add it to $50. After a few of these, watch for a pattern — there's a shortcut hiding.
The spring flood damaged stock. A rug worth $170 must be sold at a 40% discount. Find the sale price.
Work it the long way: find 40% of $170, then subtract. After a couple, watch for a shortcut — the same multiplier thinking as last chapter, with a twist.
Now the reverse problem. You're given two amounts — an original and a new — and you must find the percentage change.
A trader bought rope for $40, sold it for $52. What percent change is that?
Two steps: find the change (new − old), then work out what percent of the original the change is. That's the valpc rule from Ledger III applied to the difference.
Most students get this wrong the first time. A jacket is on sale at 20% off and now costs $80. What was the original price?
The tempting wrong answer: "add 20% back." Try it — then use the check-button to see what goes wrong.
A merchant buys goods at a cost price and sells them at a sell price. The difference is profit (or loss if the sell price is lower). Profit is usually measured as a percent of the cost.
Each problem below gives cost and sell. Find the profit or loss percentage. (Use a negative number for a loss.)
A merchant plans ahead. She paid $80 for a watch and wants a 50% profit margin. What should she charge?
This is the same multiplier move from Ledger IV (increase). A 50% markup means multiply by 1.50. Find the sell price for each cost+margin below.
The final test. Real merchants chain many operations together: discount → markup → find original price → calculate profit. You'll work through three connected scenarios using every skill you've learned.
You have worked through all ten ledgers of the Merchant's Guild.