Olympiad topic · P1–P4
Substitution
In the Hua Xia Cup's P1 to P5 papers: shapes stand for numbers, the first step towards equations.
Try one
★★ Medium△ + △ + □ = 9△ + □ = 5
Each symbol stands for a number, and the same symbol always stands for the same number. What is △?
- Hint 1: Compare the two lines: what does the first have that the second doesn't?
- Hint 2: The difference between the two results is what the extra part is worth.
- 1.The first line has one more △ than the second.
- 2.So △ = 9 − 5 = 4.
- 3.Check: □ = 5 − 4 = 1, and 4 + 4 + 1 = 9.
Answer: 4
Four levels, step by step
- ★EasyFreeUnlimited questionsOne equation.
- ★★MediumFreeUnlimited questionsTwo, by swapping or subtracting.
- ★★★HardFreeUnlimited questionsThree added together, or swapped step by step.
- ★★★★Expert (competition level)VIPUnlimited questionsThree symbols that only swap in whole groups, three products multiplied together.
Substitution: what it is and how to solve it
Each symbol stands for a number; from a few equations, find one symbol's value.
For example: △ + △ + △ = □ and □ + △ = 28. What is △? □ is three △s, so □ + △ is four △s: 28 ÷ 4 = 7.
The key idea: Swap a symbol for what it equals until only one kind is left; or add or subtract two equations. The usual method at school (from P5) uses an equation: let △ = x.
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