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    Hello, I need help in a Maths question.

    P increased by 25% is equal to Q decreased by 30%. Work out P as a percentage of Q.

    I am not sure how to work it out, maybe ratios are involved? Thank you
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    (Original post by salex413)
    Hello, I need help in a Maths question.

    P increased by 25% is equal to Q decreased by 30%. Work out P as a percentage of Q.

    I am not sure how to work it out, maybe ratios are involved? Thank you
    Can you write P increased by 25% algebraically?

    In the future, the place for maths questions is F38 (the Maths Forum).
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    P + 0.25P = Q - 0.3Q ----- Write the problem out algebraically
    P (1+ 0.25) = Q (1 - 0.3) ---------- factor out P and Q
    P (1.25) = Q (0.7) ------ do the in bracket sums/subtraction
    P = Q (0.7)/(1.25) -------- rearrange for P
    P = Q0.56 ------- answer in decimal
    Therefore P = 56%Q ----- answer as a %


    Always test to confirm solution. For example lets assume P to be 4. If P is four then P +0.25P should be 5.
    Since P= 56%Q then Q should be 7.14.
    If we put 7.14 into Q-0.3Q we should also get 5.
    7.14 - 0.3(7.14) = 7.14 - 2.14 = 5.
    Therefore solution is correct.
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    1.25P = 0.7Q

    divide by 1.25

    P = 0.56Q

    thus P = 56% of Q
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    25% increase of P can be written as 1.25 x P
    30% decrease in Q can be written as 0.7 x Q

    These are equal to each other so:
    1.25P=0.7Q

    Now isolate P (by dividing by 1.25) as you are working out P in terms of Q:
    P= 0.7Q / 1.25
    Simplified to-> P=0.56Q
    This means that P is equal to 56% of Q.
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    (Original post by frankielogue)
    ...
    Please don't post full solutions. Just give hints that nudge people towards the answer.
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    (Original post by srata)
    ...
    Please don't post full solutions. Just give hints that nudge people towards the answer.
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    (Original post by Mr M)
    Please don't post full solutions. Just give hints that nudge people towards the answer.
    sorry!
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    (Original post by Mr Optimist)
    P + 0.25P = Q - 0.3Q ----- Write the problem out algebraically
    P (1+ 0.25) = Q (1 - 0.3) ---------- factor out P and Q
    P (1.25) = Q (0.7) ------ do the in bracket sums/subtraction
    P = Q (0.7)/(1.25) -------- rearrange for P
    P = Q0.56 ------- answer in decimal
    Therefore P = 56%Q ----- answer as a %


    Always test to confirm solution. For example lets assume P to be 4. If P is four then P +0.25P should be 5.
    Since P= 56%Q then Q should be 7.14.
    If we put 7.14 into Q-0.3Q we should also get 5.
    7.14 - 0.3(7.14) = 7.14 - 2.14 = 5.
    Therefore solution is correct.
    Thank you so much! I understand it and your working out is very clear and understandable. Thanks a bunch
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    (Original post by frankielogue)
    1.25P = 0.7Q

    divide by 1.25

    P = 0.56Q

    thus P = 56% of Q
    Thank you so much! This is very helpful
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    (Original post by srata)
    25% increase of P can be written as 1.25 x P
    30% decrease in Q can be written as 0.7 x Q

    These are equal to each other so:
    1.25P=0.7Q

    Now isolate P (by dividing by 1.25) as you are working out P in terms of Q:
    P= 0.7Q / 1.25
    Simplified to-> P=0.56Q
    This means that P is equal to 56% of Q.
    Thank you for your help and working out too! Thanks a lot
 
 
 
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