Maths Olympiad Prep

Library / /54 of 168

Algebra Difficulty 1.7 Junior Find the answer

If 3+=53+\triangle=5 and +=7\triangle+\square=7, what is the value of +Δ+Δ++\triangle+\Delta+\Delta+\square+\square?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since 3+=53+\triangle=5, then =53=2\triangle=5-3=2. Since +=7\triangle+\square=7 and =2\triangle=2, then =5\square=5. Thus, +Δ+Δ++=3×2+2×5=6+10=16\triangle+\Delta+\Delta+\square+\square=3 \times 2+2 \times 5=6+10=16.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.