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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 $5$ meter long metal bar has a mass of $40 \mathrm{~kg}$ . 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. $\newline$ What is the mass of the shorter bar? $\newline$ $\mathrm{kg}$

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Solve proportions: word problems

Full solution

Q. Mandy works construction. She knows that a

5

meter long metal bar has a mass of

40 \mathrm{~kg}

. 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.

\newline

What is the mass of the shorter bar?

\newline

\mathrm{kg}

Identify Relationship: Identify the relationship between the length of the metal bar and its mass. $\newline$ Since 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 $5$ -meter-long bar, we can find the mass of a $3$ -meter-long bar by setting up a proportion.
Set Up Proportion: Set up the proportion to find the mass of the $3$ -meter-long bar. $\newline$ Let the mass of the $3$ -meter-long bar be $w$ kg. We can set up the proportion as follows: $\newline$ $\frac{5 \text{ meters}}{40 \text{ kg}} = \frac{3 \text{ meters}}{w \text{ kg}}$
Solve Proportion: Solve the proportion for $w$ . $\newline$ Cross-multiply to solve for $w$ : $\newline$ $5 \times w = 40 \times 3$
Continue Calculation: Continue the calculation to find $w$ . $\newline$ $5w = 120$ $\newline$ Now, divide both sides by $5$ to isolate $w$ : $\newline$ $w = \frac{120}{5}$ $\newline$ $w = 24$
Verify Calculation: Verify that the calculation is correct. $\newline$ The calculation seems correct as we have simply used the proportionality between the lengths and masses of the bars. Since the $5$ -meter bar is $\frac{5}{3}$ times longer than the $3$ -meter bar, the $3$ -meter bar should have $\frac{3}{5}$ times the mass of the $5$ -meter bar. Multiplying $\frac{3}{5}$ by $40$ kg gives us $24$ kg, which confirms our calculation.

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