Mathematics

Question

A number p is increased by 20%, then decrease by 10%. If the final value is 1 620, find
the original value of p.​

2 Answer

  • Increase something by its 20% means to consider its 120%:

    [tex]p\mapsto p\cdot\dfrac{120}{100} = \dfrac{120p}{100}=\dfrac{6p}{5}[/tex]

    Decrease something by its 10% means to consider its remaining 90%:

    [tex]\dfrac{6p}{5}\mapsto \dfrac{6p}{5}\cdot\dfrac{90}{100}=\dfrac{540p}{500}=\dfrac{27p}{25}[/tex]

    So, we have the equation

    [tex]\dfrac{27p}{25}=1620 \iff 27p=40500 \iff p=1500[/tex]

  • Answer:

    1500.

    Step-by-step explanation:

    We can use algebra to do this.

    20% = 0.20 and 10% = 0.10.

    We form an equation:

    p + 0.20p - 0.10(p + 0.20p) =   1620

    p + 0.20p - 0.10p - 0.02p = 1620

    1.20p - 0.12p = 1620

    1.08p = 1620

    p = 1620/1.08

    = 1500.

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