Mathematical Equations
What this question type is
A small system of linear equations using letters as unknowns. Every letter equals a unique whole number between 1 and 20, and there's exactly one solution.
How to solve it
Find the equation you can act on first — usually one that defines a letter in terms of another (like "B = 2 × A"). Substitute it into a second equation to reduce the number of unknowns, solve for one letter, then back-substitute to get the rest.
Worked example
Given B = 2 × A and B + A = 9: substitute the first into the second → 2A + A = 9 → 3A = 9 → A = 3, so B = 6.
Try it yourself
0 of 4 solved- B = 2 × A
- B + A = 9
Why
Substitute B with 2 × A in the second equation: 2A + A = 9, so 3A = 9 and A = 3. Then B = 2 × 3 = 6.
- A + 4 = B
- A + B = 14
Why
From the first equation B = A + 4. Substitute into the second: A + (A + 4) = 14, so 2A = 10 and A = 5. Then B = 9.
- C + D − A = 5
- 2 × C = D
- 7 − C = A
- 3 × C − 1 = B
Why
Solve from C. Try C = 3: D = 2 × 3 = 6, A = 7 − 3 = 4, B = 3 × 3 − 1 = 8. Check the first equation: 3 + 6 − 4 = 5 ✓. So A=4, B=8, C=3, D=6.
- B = 3 × A
- B + A = 12
Why
Substitute B with 3 × A: 3A + A = 12, so 4A = 12 and A = 3. Then B = 3 × 3 = 9.