Certainly! Let's tackle this problem step by step.
### Step-by-Step Solution
1. Convert Mixed Numbers to Improper Fractions:
- The initial weight given as [tex]\( 3 \frac{3}{2} \)[/tex] kg can be converted to an improper fraction:
[tex]\[
3 \frac{3}{2} = 3 + \frac{3}{2} = \frac{6}{2} + \frac{3}{2} = \frac{9}{2} \text{ kg}
\][/tex]
- Similarly, the weight we want to find the cost for, [tex]\( 1 \frac{3}{4} \)[/tex] kg, can be converted to an improper fraction:
[tex]\[
1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} \text{ kg}
\][/tex]
2. Determine the Cost per Kilogram:
- We know the cost for [tex]\( \frac{9}{2} \)[/tex] kg is 119 Zloty. First, calculate the cost per kilogram:
[tex]\[
\text{Cost per kilogram} = \frac{119 \text{ Zloty}}{\frac{9}{2} \text{ kg}} = \frac{119}{\frac{9}{2}} = \frac{119 \times 2}{9} = \frac{238}{9} \approx 26.44 \text{ Zloty/kg}
\][/tex]
3. Calculate the Cost for [tex]\( \frac{7}{4} \)[/tex] kg:
- Now, we use the cost per kilogram to find the cost for [tex]\( \frac{7}{4} \)[/tex] kg:
[tex]\[
\text{Cost for } \frac{7}{4} \text{ kg} = \left( \frac{238}{9} \text{ Zloty/kg} \right) \times \frac{7}{4} \text{ kg} = \frac{238 \times 7}{9 \times 4} = \frac{1666}{36} \approx 46.278 \text{ Zloty}
\][/tex]
So, the cost of [tex]\(1 \frac{3}{4} \text{ kg}\)[/tex] of luger is approximately 46.28 Zloty.
