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Emanuel was charged 
$32 for a 
14(2)/(9)km taxi ride. The cost per kilometer is constant.
What was the cost per kilometer? 
$

Emanuel was charged $32 \$ 32 for a 1429 km 14 \frac{2}{9} \mathrm{~km} taxi ride. The cost per kilometer is constant.\newlineWhat was the cost per kilometer? \newline$ \$

Full solution

Q. Emanuel was charged $32 \$ 32 for a 1429 km 14 \frac{2}{9} \mathrm{~km} taxi ride. The cost per kilometer is constant.\newlineWhat was the cost per kilometer? \newline$ \$
  1. Convert to Improper Fraction: Convert the mixed number to an improper fraction to find the total distance in kilometers.\newline14(29)14\left(\frac{2}{9}\right) km is the same as (14×9+2)/9\left(14 \times 9 + 2\right)/9 km, which equals (126+2)/9\left(126 + 2\right)/9 km, or 1289\frac{128}{9} km.
  2. Calculate Cost per Kilometer: Calculate the cost per kilometer by dividing the total cost by the total distance.\newlineThe cost per kilometer is $32\$32 divided by 1289\frac{128}{9} kilometers.\newlineTo divide by a fraction, multiply by its reciprocal. So, $32×9128=$32×9/128\$32 \times \frac{9}{128} = \$32 \times 9 / 128.
  3. Perform Multiplication and Division: Perform the multiplication and division to find the cost per kilometer.\newline$32×9=$288\$32 \times 9 = \$288, and $288/128=$2.25\$288 / 128 = \$2.25.\newlineSo, the cost per kilometer is $2.25\$2.25.

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