Weighing Numbers

Algebra Level pending

A square is on a balanced scale with 5 circles on the other side. A circle is on another balanced scale along with 2 triangles. Another balanced scale shows that a triangle equals 5 grams, and one last one shows that a square and a trapezoid equal 386 grams. What is the weight of the trapezoid?

325 grams 367 grams 336 grams It's not possible to find this out 297 grams 354 grams

Alan Vu by Alan Vu , 13, USA

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3 solutions

Saya Suka
May 28, 2021

🟦 = 🔴🔴🔴🔴🔴
🔴 = ⚠️⚠️
⚠️ = 5
🔴 = 2 × 5 = 10
🟦 = 5 × 10 = 50

🟦🔈 = 386 = 50 + 🔈
🔈 = 386 – 50 = 336

1 Helpful 1 Interesting 2 Brilliant 0 Confused
Andrei Zonga
May 29, 2021

Call S the square, C the circle, T1 the triangle and T2 the trapezoid. Then, we have the following equations: S=5C (i) C=2T1 (ii) T1=5 (iii) S+T2=386 (iv) From (iii) and (ii) C=2 5=10 (v) From (v) and (i) S=5 10=50 (vi) From (vi) and (iv) 50+T2=386. Subtract 50 from both sides: T2=336 Done!

1 Helpful 1 Interesting 1 Brilliant 0 Confused
Aditya Mittal
Jun 6, 2021

Scale 1 Scale 1

scale 2 scale 2

scale 3 scale 3

scale 4 scale 4

From scale 1, 2 and 3, we get 1 S Q U A R E = 50 g r a m s 1 SQUARE = 50 grams

And using 4 scale, we get 1 T R A P E Z O I D = 386 − 50 = 336 g 1 TRAPEZOID = 386-50 = 336 g

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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