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What single decimal multiplier would you use to increase by 5% followed by a 15% increase?

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Answer:

(1.2075)

Explanation:

Lets assume we are increasing a price on a $100 item to help visualize the steps.

The two steps of 5% and then 15% can each be expressed as:

5%: (1+0.05) [The 1 represents the fact that the final cost is full price (1) plus 5%(0.05)]

15% (1+0.15) [Same explanation, but now with 0.15 for 15%]

We can apply these factors individually:

Assume a base of $100:

5% increase would make it $105 [$100*(1.05)=$105]

15% increase: On top of the 5%, we would go to: $105*(1.15) = $120.75

Or we can use a single multiplier.

If we look at the steps from above, we see that the algebra consisted of taking the origianl price ($100) and multiplying it twice: once with (1+0.05) and once with (1+1.15). Write this in the form of an equation:

($100)*(1+0.05)*(1+0.15) = $120.75

Let's multiply (1+0.05)*(1+0.15)

= (1.2075)

We can use this single factor (multiplier) to find the correct/same value as before:

(1.2075)($100) = $120.75

User Amit Madan
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