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.​

Answer 1

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

$p\mapsto p\cdot\dfrac{120}{100} = \dfrac{120p}{100}=\dfrac{6p}{5}$

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

$\dfrac{6p}{5}\mapsto \dfrac{6p}{5}\cdot\dfrac{90}{100}=\dfrac{540p}{500}=\dfrac{27p}{25}$

So, we have the equation

$\dfrac{27p}{25}=1620 \iff 27p=40500 \iff p=1500$

Answer 2

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.