Track metal amounts through three alloys · source reference

Printed question

A piece of alloy made from gold, silver and bronze weighs 136 g. A second piece of alloy weighs 323 g and contains the same amount of gold, twice as much silver, and three times as much bronze as the first piece. A third piece of alloy weighs 238 g and contains 4 times as much gold, one third as much silver, and same amount of bronze as the second piece. Find the respective amounts of gold, silver and bronze used in the first piece of alloy. [3]

[2009/RJC/Promo/1]

Printed working

Let $x,y,z$ be the respective amounts (in grams) of gold, silver and bronze used in the first piece of alloy. Then

$$x+y+z=136,$$ $$x+2y+3z=323,$$ $$4x+\frac23y+3z=238.$$

Use calculator to obtain $x=5,y=75,z=56$. So the first piece of alloy uses 5 g of gold, 75 g of silver, 56 g of bronze.

Teacher notes

Step 1: Identify all unknowns. Define the variables.

Step 2: Formulate the equations.

Step 3: Solve the equations. Use GC: Go to apps → 9↓PlySmlt2 → 2: Simultaneous Eqn Solver → Eqns “3”, Unknowns “3” … → Key in coefficients and values, then press “Solve”.

Step 4: Interpret the solution based on the given context.

Printed answer key

5 g of gold, 75 g of silver, 56 g of bronze.

Source provenance

2025 TJC H2 Math (9758) JC2 MSM: EQUATIONS. Question sheet printed pages 15–19; solution sheet printed pages 1–12. Original exam attribution is retained above. Currency dollar signs are spelled out outside maths to avoid confusing currency with TeX delimiters.