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Secondary rarr Number rarr Ratio & Proportion 464d: Determine an amount given a change in a Watch Worked Example ratio where one part is changing. Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 COMPLETION 60% There are blue counters and black counters in a bag in the ratio 5:1 34 blue counters are removed and the ratio becomes 3:4 Work out how many black counters there are in the bag. black counters Submit Answer

Secondary → \rightarrow Number → \rightarrow Ratio \& Proportion\newline464464d: Determine an amount given a change in a\newlineWatch Worked Example\newlineratio where one part is changing.\newlineQ11\newlineQ22\newlineQ33\newlineQ44\newlineQ55\newlineQ66\newlineQ77\newlineQ88\newlineQ99\newlineQ1010\newlineQ1111\newlineQ1212\newlineQ1313\newlineQ1414\newlineQ1515\newlineQ1616\newlineQ1717\newlineQ1818\newlineQ1919\newlineQ2020\newlineCOMPLETION\newline60% 60 \% \newlineThere are blue counters and black counters in a bag in the ratio 5:1 5: 1 \newline3434 blue counters are removed and the ratio becomes 3:4 3: 4 \newlineWork out how many black counters there are in the bag.\newlineblack counters\newlineSubmit Answer

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Q. Secondary → \rightarrow Number → \rightarrow Ratio \& Proportion\newline464464d: Determine an amount given a change in a\newlineWatch Worked Example\newlineratio where one part is changing.\newlineQ11\newlineQ22\newlineQ33\newlineQ44\newlineQ55\newlineQ66\newlineQ77\newlineQ88\newlineQ99\newlineQ1010\newlineQ1111\newlineQ1212\newlineQ1313\newlineQ1414\newlineQ1515\newlineQ1616\newlineQ1717\newlineQ1818\newlineQ1919\newlineQ2020\newlineCOMPLETION\newline60% 60 \% \newlineThere are blue counters and black counters in a bag in the ratio 5:1 5: 1 \newline3434 blue counters are removed and the ratio becomes 3:4 3: 4 \newlineWork out how many black counters there are in the bag.\newlineblack counters\newlineSubmit Answer
  1. Initial ratio setup: Initial ratio of blue to black counters is 5:15:1. This means for every 55 blue counters, there is 11 black counter. Let the number of black counters be bb. Then, the number of blue counters is 5b5b.
  2. New ratio setup: After removing 3434 blue counters, the new ratio of blue to black counters becomes 3:43:4. So, the new number of blue counters is 5b−345b - 34. The equation based on the new ratio is 5b−34b=34\frac{5b - 34}{b} = \frac{3}{4}.
  3. Solve for b: Solve the equation (5b−34)/b=3/4(5b - 34)/b = 3/4 for b. Cross-multiplying gives 4(5b−34)=3b4(5b - 34) = 3b. Simplifying, 20b−136=3b20b - 136 = 3b.
  4. Final solution: Further simplifying, 20b−3b=13620b - 3b = 136, 17b=13617b = 136, b=13617b = \frac{136}{17}, b=8b = 8.

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