High School

Quincy is trying to estimate the height of a tree in his backyard. He measures the tree’s shadow as 12 ft. He stands near the tree and measures his own shadow as 3 ft. Quincy knows that he is about 5 ft tall. He estimates the height of the tree by following these steps:

Step 1: Set up a proportion \(\frac{x}{12} = \frac{5}{3}\)

Step 2: Cross multiply \(5 \times 12 = 3x\)

Step 3: Simplify \(60 = 3x\)

Step 4: Solve for \(x\) \(\frac{60}{3} = x\) \(\Rightarrow x = 20 \text{ feet}\)

In which step, if any, did Quincy make a mistake?

Answer :

Answer:

In step 1 did Quincy make a mistake

Step-by-step explanation:

Proportions states that two ratios or fractions are equal.

As per the statement:

Shadow of the tree = 12 ft

Shadow of Quincy = 3 ft

Height of the Quincy = 5 ft tall

let x be the height of the tree.

By definition of proportions;

[tex]\frac{\text{Height of the tree}}{\text{Height of the Quincy}}=\frac{\text{Shadow of the tree}}{\text{Shadow of the Quincy}}[/tex]

then;

[tex]\frac{x}{5} = \frac{12}{3}[/tex]

By cross multiply we have;

[tex]3x = 60[/tex]

Divide both sides by 3 we have;

x = 20 ft

Since, he made mistake in step 1.

The following correct steps are:

Step 1:

Set up a proportion

[tex]\frac{x}{5} = \frac{12}{3}[/tex]

Step 2:

Cross multiply

[tex]3x = 12 \times 5[/tex]

Step 3:

Simplify:

[tex]3x = 60[/tex]

Step 4:

Solve for x:

x = 20 ft

Quincy made a mistake in Step 1. The correct proportion is actually

[tex]\frac{x}{12}[/tex] = [tex]\frac{5}{3}[/tex] .

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