# Lesson 12

Applications of Arithmetic with Powers of 10

### Problem 1

Which is larger: the number of meters across the Milky Way, or the number of cells in all humans? Explain or show your reasoning.

Some useful information:

• The Milky Way is about 100,000 light years across.
• There are about 37 trillion cells in a human body.
• One light year is about $$10^{16}$$ meters.
• The world population is about 7 billion.

### Solution

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### Problem 2

Ecologists measure the body length and wingspan of 127 butterfly specimens caught in a single field.

1. Draw a line that you think is a good fit for the data.
2. Write an equation for the line.

3. What does the slope of the line tell you about the wingspans and lengths of these butterflies?

### Solution

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(From Unit 6, Lesson 5.)

### Problem 3

Diego was solving an equation, but when he checked his answer, he saw his solution was incorrect. He knows he made a mistake, but he can’t find it. Where is Diego’s mistake and what is the solution to the equation?

\displaystyle \begin{align} \text-4(7-2x)=3(x+4)\\ \text-28-8x=3x+12\\ \text-28=11x+12\\ \text-40=11x\\ \text{-}\frac {40}{11}=x\ \end{align}

### Solution

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(From Unit 4, Lesson 5.)

### Problem 4

The two triangles are similar. Find $$x$$.

### Solution

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(From Unit 2, Lesson 7.)