When a Increases by 18% then B increases by 16% and when 8 increases by 18% then C increases by 9% a is increased from 32 to 48 C must therefore increase from 80 to?

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Tutorial: Percentage Increases & Decreases - Percentage Multipliers

To calculate percentage increases and decreases, we use Percentage multipliers. Percentage multipliers allow us to calculate percentage increases and percentage decreases very quickly, with one single multiplication.

By the end of this section we'll know how to find percentage multipliers as well as calculate any percentage increase, or decrease, such as:

Increasing $48$ by $35\%$ or Decreasing $220$ by $40\%$ We start by watching the following tutorial.

Tutorial: Percentage Increases & Decreases - Percentage Multipliers

In the following tutorial we learn how to calculate percentage increases and decreases using percentage multipliers.

The method shown in the tutorial is summarized here in three steps.

To increase, or decrease a number $N$, by a percentage $X\% $ we multiply $N$ by a percentage multiplier (often just called multiplier).

We can calculate any percentage increase, or decrease, in three steps:

Step 1: write $X\% $ in decimal form. Remember, this is done by moving the number $X$ back two decimal places.
Example: $5\% = 0.05$, $12\% = 0.12$, ... .
Step 2: Calculate the percentage multiplier by adding, or subtracting, the decimal found in step 1 to, or from, $1$
- For percentage increases: add the decimal to $1$.
- For percentage decreases: subtract the decimal from $1$.
Step 3: multiply the number $N$ by the multiplier, found in Step 2.

Increase $80$ kg by $23\% $.

Solution

We follow our three-step method:

Step 1: we write $23\%$ in decimal form: \[23\% = 0.23\]
Step 2: we find the multiplier. Since we're increasing by $23\%$, we add $0.23$ to $1$: \[1 + 0.23 = 1.23\]
Step 3: we multiply $80$ by the multiplier $1.23$: \[80 \times 1.23 = 98.4\] So $80$kg increased by $23\%$ is $98.4$ kg.

Decrease $\$ \ 120$ by $19\% $.

Solution

We follow our three-step method:

Step 1: we write $19\%$ in decimal form: \[19\% = 0.19\]
Step 2: we find the multiplier. Since we're decreasing by $19\%$, we subtract $0.19$ from $1$: \[1 - 0.19 = 0.81 \]
Step 3: we multiply $80$ by the multiplier $0.81$: \[120 \times 0.81 = 97.2\] So $\$ \ 120$ decreased by $19\%$ is $\$ \ 97.20$.