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Math  /  Algebra

QuestionCarys calculates the total amount EE, in dollars, that she earns for working hh hours using the equation E=10hE=10 h.
How many dollars does Carys earn per hour? □\square dollars At that rate, how many hours does it take Carys to earn one dollar? □\square hours

Studdy Solution

STEP 1

What is this asking? How much does Carys earn each hour, and how long does it take her to earn $1\$1? Watch out! Don't mix up the earnings per hour and the hours per dollar!

STEP 2

1. Dollars Earned Per Hour
2. Hours Per Dollar

STEP 3

Alright, let's **decode** this equation: E=10hE = 10h.
This tells us that Carys's **total earnings** (EE) are equal to **10 times** the **number of hours** (hh) she works.

STEP 4

So, if Carys works **1 hour**, she earns E=10⋅1=$10E = 10 \cdot 1 = \$10.

STEP 5

That means Carys earns $10\$10 per hour!

STEP 6

Now, we want to figure out how long it takes Carys to earn just $1\$1.
We know she earns $10\$10 in one hour.

STEP 7

Let's set up a **proportion**: $101 hour=$1x hours \frac{\$10}{1 \text{ hour}} = \frac{\$1}{x \text{ hours}} where xx is the **number of hours** it takes to earn $1\$1.

STEP 8

**Cross-multiply**: $10⋅x=$1⋅1 \$10 \cdot x = \$1 \cdot 1 10x=1 10x = 1

STEP 9

**Divide both sides** of the equation by **10** to solve for xx: 10x10=110 \frac{10x}{10} = \frac{1}{10} x=110 x = \frac{1}{10}

STEP 10

So, it takes Carys 110\frac{1}{10} of an hour to earn $1\$1!

STEP 11

Carys earns $10\$10 per hour.
It takes her 110\frac{1}{10} of an hour to earn $1\$1.

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