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Mandy works construction. She knows that a 5 meter long metal bar has a mass of 
40kg. Mandy wants to figure out the mass 
(w) of a bar made out of the same metal that is 3 meters long and the same thickness.
What is the mass of the shorter bar?

kg

Mandy works construction. She knows that a 55 meter long metal bar has a mass of 40 kg 40 \mathrm{~kg} . Mandy wants to figure out the mass (w) (w) of a bar made out of the same metal that is 33 meters long and the same thickness.\newlineWhat is the mass of the shorter bar?\newlinekg \mathrm{kg}

Full solution

Q. Mandy works construction. She knows that a 55 meter long metal bar has a mass of 40 kg 40 \mathrm{~kg} . Mandy wants to figure out the mass (w) (w) of a bar made out of the same metal that is 33 meters long and the same thickness.\newlineWhat is the mass of the shorter bar?\newlinekg \mathrm{kg}
  1. Identify Relationship: Identify the relationship between the length of the metal bar and its mass.\newlineSince the metal bars are made of the same material and have the same thickness, the mass of the metal bar is directly proportional to its length. This means that if we know the mass of a 55-meter-long bar, we can find the mass of a 33-meter-long bar by setting up a proportion.
  2. Set Up Proportion: Set up the proportion to find the mass of the 33-meter-long bar.\newlineLet the mass of the 33-meter-long bar be w w kg. We can set up the proportion as follows:\newline5 meters40 kg=3 metersw kg \frac{5 \text{ meters}}{40 \text{ kg}} = \frac{3 \text{ meters}}{w \text{ kg}}
  3. Solve Proportion: Solve the proportion for w w .\newlineCross-multiply to solve for w w :\newline5×w=40×3 5 \times w = 40 \times 3
  4. Continue Calculation: Continue the calculation to find w w .\newline5w=120 5w = 120 \newlineNow, divide both sides by 55 to isolate w w :\newlinew=1205 w = \frac{120}{5} \newlinew=24 w = 24
  5. Verify Calculation: Verify that the calculation is correct.\newlineThe calculation seems correct as we have simply used the proportionality between the lengths and masses of the bars. Since the 55-meter bar is 53 \frac{5}{3} times longer than the 33-meter bar, the 33-meter bar should have 35 \frac{3}{5} times the mass of the 55-meter bar. Multiplying 35 \frac{3}{5} by 4040 kg gives us 2424 kg, which confirms our calculation.

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