What two facts settle, step by step
Three teas, two coffees and one cocoa come to 96c.
What do one tea, one coffee and one cocoa cost altogether?
Subtract the facts, not the prices
- Two totals and three unknown prices: 4 teas, 1 coffee and 3 cocoas come to 275c, and 3 teas and 2 cocoas come to 159c. The question wants 1 tea, 1 coffee and 1 cocoa.
- Do not go looking for the prices. Three unknowns and two facts means they cannot be found, and a child who spends the page trying has been beaten by a question that never wanted them.
- Take fact 2 away from fact 1, which is allowed because both are true at once: what one basket has over the other costs what one total has over the other. Everything shared by the two cancels, and what is left is a basket nobody was told the price of.
- That leaves 1 tea, 1 coffee and 1 cocoa, costing 116c. The answer came from the two totals alone — no price was ever found, and none was needed.
How it works.
- 01
Two totals and three unknown prices: 4 teas, 1 coffee and 3 cocoas come to 275c, and 3 teas and 2 cocoas come to 159c. The question wants 1 tea, 1 coffee and 1 cocoa.
- 02
Do not go looking for the prices. Three unknowns and two facts means they cannot be found, and a child who spends the page trying has been beaten by a question that never wanted them.
- 03
Take fact 2 away from fact 1, which is allowed because both are true at once: what one basket has over the other costs what one total has over the other. Everything shared by the two cancels, and what is left is a basket nobody was told the price of.
- 04
That leaves 1 tea, 1 coffee and 1 cocoa, costing 116c. The answer came from the two totals alone — no price was ever found, and none was needed.