What two facts settle
The question
The cafe board has lost its prices. Fact 1: 4 teas, 1 coffee and 3 cocoas come to 275c. Fact 2: 3 teas and 2 cocoas come to 159c.
What do one tea, one coffee and one cocoa cost altogether?
Subtract the facts, not the prices
4 teas, 1 coffee and 3 cocoas=275c
3 teas and 2 cocoas=159c
3 unknowns·2 facts
275c−159c=116c
1 tea, 1 coffee and 1 cocoa=116c
- 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.
- Three prices and two facts means the single prices cannot be found — and you do not need them.
- Take fact 2 away from fact 1: what one basket has extra costs what one total has extra. Everything the baskets share cancels.
- That leaves 1 tea, 1 coffee and 1 cocoa, costing 116c. No single price 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
Three prices and two facts means the single prices cannot be found — and you do not need them.
- 03
Take fact 2 away from fact 1: what one basket has extra costs what one total has extra. Everything the baskets share cancels.
- 04
That leaves 1 tea, 1 coffee and 1 cocoa, costing 116c. No single price was needed.