Question

lesson summary
the scale factor is the number that determines whether the new drawing is an enlargement or a reduction of the
original. if the scale factor is greater than 100%, then the resulting drawing is an enlargement of the original
drawing. if the scale factor is less than 100%, then the resulting drawing is a reduction of the original drawing.
to compute actual lengths from a scale drawing, a scale factor must first be determined. to do this, use the
relationship quantity = percent × whole, where the original drawing represents the whole and the scale drawing
represents the quantity. once a scale factor is determined, then the relationship
quantity = percent × whole can be used again using the scale factor as the percent, the actual length from the
original drawing as the whole, and the actual length of the scale drawing as the quantity.

problem set

1. the smaller train is a scale drawing of the larger train. if the length of the tire rod connecting the three tires of the

larger train, as shown below, is 36 inches, write an equation to find the length of the tire rod of the smaller train.
interpret your solution in the context of the problem.

Explanation:

Step1: Find the scale factor

The scale factor is the ratio of the scale drawing length to the original length.
$\text{Scale Factor} = \frac{\text{Smaller train's marked length}}{\text{Larger train's marked length}} = \frac{6}{16} = \frac{3}{8}$

Step2: Set up the equation for tire rod

Let $x$ = smaller train's tire rod length. Use $\text{Quantity} = \text{Percent} \times \text{Whole}$, where the whole is the larger train's tire rod length.
$x = \frac{3}{8} \times 36$

Step3: Calculate the value of $x$

Simplify the expression to find $x$.
$x = \frac{3 \times 36}{8} = \frac{108}{8} = 13.5$

Answer:

The equation to find the length of the smaller train's tire rod is $x = \frac{3}{8} \times 36$, where $x$ represents the length of the smaller train's tire rod. The length of the tire rod for the smaller train is 13.5 inches, meaning the smaller train's tire rod is a scaled-down (reduced) version of the larger train's 36-inch tire rod, using a scale factor of $\frac{3}{8}$.