GCSEMathsAQAHigherFlashcards3. Ratio, Proportion & Rates of ChangeProblem Solving with Ratios

Problem Solving with Ratios (AQA GCSE Maths)

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  • FrontRatios with Fractions, Decimals & Percentages

    A bag contains blue and red marbles in the ratio 3 : 5.

    If 20% of blue marbles are cracked, what percentage of the bag of marbles are blue and cracked?

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  • A bag contains blue and red marbles in the ratio 3 : 5.

    If 20% of blue marbles are cracked, what percentage of the bag of marbles are blue and cracked?

    The ratio 3 : 5 can be written as a fraction (there are 3 + 5 = 8 parts).

    So 3 over 8 of the bag are blue marbles.

    20% of blue marbles are cracked, so find 20% of 3 over 8, for example 20 over 100 cross times 3 over 8.

    This gives 3 over 40 equals 0.075 so 7.5% are blue and cracked.

  • A bag contains blue and red marbles in the ratio 3 : 5.

    If 4 over 25 of the red marbles are cracked, find the fraction of the bag of marbles that are cracked red marbles.

    The ratio 3 : 5 can be written as a fraction (there are 3 + 5 = 8 parts).

    So 5 over 8 of the bag are red marbles.

    4 over 25 of the red marbles are cracked, so find 4 over 25 of 5 over 8, for example 4 over 25 cross times 5 over 8.

    This gives 1 over 10 which is the fraction of the bag of marbles that are red and cracked.

  • True or False?

    If a ratio question wants a fraction or percentage answer, you can sometimes choose your own total number of items to do the working (e.g. assume there are 100 pupils in the school).

    True.

    If a ratio question wants a fraction or percentage answer, you can sometimes choose your own total number of items to do the working (e.g. assume there are 100 pupils in the school).

  • Given two, two-part ratios that share different amounts of a common quantity, how can they be combined into a single three -part ratio?

    E.g. if x space colon space y space equals space 1 space colon thin space 3 and y space colon thin space z space equals space 2 space colon thin space 5, what is the combined ratio x space colon thin space y space colon space z?

    To combine two, two-part ratios into a single three-part ratio:

    1. Find equivalent ratios so that the value for y is the same for both.

    2. Join the two ratios by their common quantity.

    E.g.
    x space colon space y space equals space 1 cross times 2 space colon thin space 3 cross times 2 space equals space 2 space colon space 6
    y space colon space z space equals space 2 cross times 3 space colon thin space 5 cross times 3 space equals space 6 space colon space 15

    So, x space colon space y space colon space z space equals space 2 space colon space 6 space colon space 15

  • True or False?

    If x space colon space y space equals space 1 space colon thin space 3 and x space colon thin space z space equals space 1 space colon thin space 2, then x space colon thin space y space colon space z equals 1 space colon space 3 space colon space 2.

    True.

    If x space colon space y space equals space 1 space colon thin space 3 and x space colon thin space z space equals space 1 space colon thin space 2, then x space colon thin space y space colon space z equals 1 space colon space 3 space colon space 2.

    In both original two-part ratios, the quantity x has the same value of 1, so no equivalent ratios need to be found.

    The three quantities can be written in the required order as a single three-part ratio.

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