Optional enrichment: Changing ratios, inverse variation and joint proportion
Example 1
y=zcx2 for a constant c. When x=4 and z=5,y=16. Later y=320 and z=25. Find the positive new value of x.
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Answer: 40
- The first case gives c=5.
- Then x2=cyz=1600.
- Take the positive square root: x=40.
Example 2
A tank initially contains V litres of well-mixed red and blue dye in the ratio 2:3. Remove 6L of the mixture and replace it with 6L of pure blue dye, mixing fully. Repeat this once. The final red:blue ratio is 72:173. Find V, with V>6.
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Answer: 42
- Each replacement multiplies the red fraction by (1−V6).
- Thus (52)(1−V6)2=24572.
- Because V>6, take the positive square root and solve to obtain V=42L.
Example 3
y=zcx2 for a constant c. When x=4 and z=5,y=548. Later y=192 and z=25. Find the positive new value of x.
Show worked answer
Answer: 40
- The first case gives c=3.
- Then x2=cyz=1600.
- Take the positive square root: x=40.