Rocket fans out a deck of index cards. "Twenty cards between us. I hold four more than you. How many each?"
"Two unknowns," Raven says. "Call mine y and yours x. What do you notice we know?"
"x + y = 20," Rocket says. "And x - y = 4. Two equations."
"Then solve it like yesterday," Raven says. "x = y + 4 from the second. Put it into the first."
"y + 4 + y = 20. So 2y = 16 and y = 8. Then x = 12." Rocket counts his cards. Twelve.
Nova hovers over the deck, her light splitting it into two uneven piles. "Would one equation have been enough?"
"No," Raven says. "x + y = 20 has lots of answers. The second equation picks out one."
"Two unknowns, two equations," Rocket says. "That is the rule."
A puzzle with two unknown numbers needs two facts about them. Each fact becomes an equation.
Rocket and Raven: x + y = 20 says the total. x - y = 4 says the difference. The solution is (12, 8).
Name the unknowns first, write both facts as equations, then solve by substitution and check in the story.
The crew wrote four puzzles for Puzzle Night. Every count is the crew's own, made up for the Puzzle Post.
| Puzzle | The facts | System | Answer |
|---|---|---|---|
| Rocket and Raven | Rocket and Raven hold 20 cards between them. Rocket holds 4 more than Raven. | x + y = 20, x - y = 4 | Rocket 12, Raven 8 |
| Red and blue beans | A cup holds 15 beans, red and blue. There are twice as many red as blue. | x + y = 15, x = 2y | red 10, blue 5 |
| Steps and jumps | Rocket crossed the garage in 12 moves, steps and jumps. A step is 1 tile, a jump is 3 tiles, and he covered 20 tiles. | x + y = 12, x + 3y = 20 | ? |
| Two timers | Two timers together ring for 30 minutes. One rings 6 minutes longer than the other. | x + y = 30, x - y = 6 | ? |
Sharp puzzle writing. Tomorrow you meet systems in everyday life and review the week.