Question
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Increase 99 in the ratio \( 12: 11 \)

Ask by Kirk Stephens. in South Africa
Mar 09,2025

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Tutor-Verified Answer

Answer

The increased value is 108.

Solution

Let the new value be \( x \). According to the ratio \(12:11\), we have: \[ \frac{x}{99}=\frac{12}{11} \] Step 1: Isolate \( x \): \[ x=\frac{12}{11}\times99 \] Step 2: Simplify the expression: \[ x=\frac{12\times99}{11}=\frac{12\times(11\times9)}{11}=12\times9=108 \] Thus, the increased value is \( 108 \).

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The Deep Dive

To increase 99 in the ratio \( 12: 11 \), first, we need to find out how much of an increase is represented by that ratio. The sum of the parts of the ratio \( 12 + 11 = 23 \). Next, we take the difference between the parts of the ratio, which is \( 12 - 11 = 1 \). Now, we can calculate the increase: 1. Calculate the increase: \[ \text{Increase} = 99 \times \frac{1}{23} \approx 4.3043 \] 2. So, the new total is \[ 99 + 4.3043 \approx 103.3043 \] To express it more simply, increasing 99 in the ratio \( 12: 11 \) leads to a new value of roughly 103.30. You could say that if it were a race, 99 just got a little boost to hit 103.30 while still keeping pace in that ratio!

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