To find the percentage increase for an item that originally cost [tex]$12 and now costs $[/tex]21, follow these steps:
1. First, determine the increase in cost.
The new cost is [tex]$21, and the original cost is $[/tex]12.
Hence, the increase in cost is calculated as:
\( \text{increase} = \text{new cost} - \text{original cost} \)
[tex]\[ \text{increase} = 21 - 12 \][/tex]
[tex]\[ \text{increase} = 9 \][/tex]
2. Next, calculate the percentage increase relative to the original cost.
The formula for the percentage increase is:
[tex]\[ \text{percentage increase} = \left( \frac{\text{increase}}{\text{original cost}} \right) \times 100 \][/tex]
Plugging in the values:
[tex]\[ \text{percentage increase} = \left( \frac{9}{12} \right) \times 100 \][/tex]
3. Divide the increase by the original cost to get a decimal:
[tex]\[ \frac{9}{12} = 0.75 \][/tex]
4. Multiply this result by 100 to convert it to a percentage:
[tex]\[ 0.75 \times 100 = 75 \][/tex]
5. Finally, round the percentage to 3 decimal places if necessary, but in this case, the result is already a whole number:
[tex]\[ 75.000 \][/tex]
Therefore, the percentage increase in the cost of the item is 75.000 (when rounded to 3 decimal places).
