Math / Algebra

QuestionUse the five-step strategy for solving word problems to find the number described. When $30 \%$ of a number is added to the number, the result is 143 .
What is the number? $\square$

Studdy Solution

STEP 1

What is this asking? We need to find a number such that when 30% of itself is added to it, the result is 143. Watch out! Don't forget that adding 30% of a number to itself isn't the same as finding 30% of 143!

STEP 2

1. Set up the equation
2. Solve for $x$

STEP 3

Let $x$ be the mystery number we're trying to find.
This is our starting point!

STEP 4

30% of $x$ can be written as $0.30 \cdot x$ or just $0.3x$ .
Remember, "percent" means "per hundred," so 30% is the same as $\frac{30}{100}$ , which simplifies to $0.3$ .

STEP 5

The problem says "when 30% of a number is added to the number, the result is 143." We can write this as an equation: $x + 0.3x = 143$ .
This equation perfectly captures the problem's information!

STEP 6

We've got $x + 0.3x$ .
Remember that $x$ is the same as $1 \cdot x$ , so $x + 0.3x$ is the same as $1x + 0.3x = 1.3x$ .
So, our equation becomes $1.3x = 143$ .

STEP 7

To get $x$ by itself, we need to divide both sides of the equation by 1.3.
This is because $\frac{1.3}{1.3} = 1$ , effectively turning the left side into $1 \cdot x$ , which is just $x$ .
Remember, what we do to one side of the equation, we must do to the other to keep things balanced!

STEP 8

Now, we have $x = \frac{143}{1.3}$ .
Let's do the division: $\frac{143}{1.3} = \frac{143}{\frac{13}{10}} = \frac{143}{1} \cdot \frac{10}{13} = \frac{1430}{13} = 110$ .
So, $x = \textbf{110}$ !
We found our mystery number!

STEP 9

The number is $\boxed{110}$ .

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QuestionUse the five-step strategy for solving word problems to find the number described. When $30 \%$ of a number is added to the number, the result is 143 .
What is the number? $\square$

Studdy Solution

STEP 1

What is this asking? We need to find a number such that when 30% of itself is added to it, the result is 143. Watch out! Don't forget that adding 30% of a number to itself isn't the same as finding 30% of 143!

STEP 2

1. Set up the equation
2. Solve for $x$

STEP 3

Let $x$ be the mystery number we're trying to find.
This is our starting point!

STEP 4

30% of $x$ can be written as $0.30 \cdot x$ or just $0.3x$ .
Remember, "percent" means "per hundred," so 30% is the same as $\frac{30}{100}$ , which simplifies to $0.3$ .

STEP 5

The problem says "when 30% of a number is added to the number, the result is 143." We can write this as an equation: $x + 0.3x = 143$ .
This equation perfectly captures the problem's information!

STEP 6

We've got $x + 0.3x$ .
Remember that $x$ is the same as $1 \cdot x$ , so $x + 0.3x$ is the same as $1x + 0.3x = 1.3x$ .
So, our equation becomes $1.3x = 143$ .

STEP 7

To get $x$ by itself, we need to divide both sides of the equation by 1.3.
This is because $\frac{1.3}{1.3} = 1$ , effectively turning the left side into $1 \cdot x$ , which is just $x$ .
Remember, what we do to one side of the equation, we must do to the other to keep things balanced!

STEP 8

Now, we have $x = \frac{143}{1.3}$ .
Let's do the division: $\frac{143}{1.3} = \frac{143}{\frac{13}{10}} = \frac{143}{1} \cdot \frac{10}{13} = \frac{1430}{13} = 110$ .
So, $x = \textbf{110}$ !
We found our mystery number!

STEP 9

The number is $\boxed{110}$ .

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QuestionUse the five-step strategy for solving word problems to find the number described. When 30%30 \%30% of a number is added to the number, the result is 143 .What is the number? □\square□

Studdy Solution

STEP 1

What is this asking? We need to find a number such that when 30% of itself is added to it, the result is 143. Watch out! Don't forget that adding 30% of a number to itself isn't the same as finding 30% of 143!

STEP 2

1. Set up the equation2. Solve for xxx

STEP 3

Let xxx be the **mystery number** we're trying to find.This is our **starting point**!

STEP 4

30% of xxx can be written as 0.30⋅x0.30 \cdot x0.30⋅x or just 0.3x0.3x0.3x.Remember, "percent" means "per hundred," so 30% is the same as 30100\frac{30}{100}10030​, which simplifies to 0.30.30.3.

STEP 5

The problem says "when 30% of a number is *added* to the number, the result is 143." We can write this as an equation: x+0.3x=143x + 0.3x = 143x+0.3x=143.This equation perfectly captures the problem's information!

STEP 6

We've got x+0.3xx + 0.3xx+0.3x.Remember that xxx is the same as 1⋅x1 \cdot x1⋅x, so x+0.3xx + 0.3xx+0.3x is the same as 1x+0.3x=1.3x1x + 0.3x = 1.3x1x+0.3x=1.3x.So, our equation becomes 1.3x=1431.3x = 1431.3x=143.

STEP 7

STEP 8

STEP 9

The number is 110\boxed{110}110​.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionUse the five-step strategy for solving word problems to find the number described. When $30 \%$ of a number is added to the number, the result is 143 .
What is the number? $\square$

1. Set up the equation
2. Solve for $x$

Let $x$ be the mystery number we're trying to find.
This is our starting point!

30% of $x$ can be written as $0.30 \cdot x$ or just $0.3x$ .
Remember, "percent" means "per hundred," so 30% is the same as $\frac{30}{100}$ , which simplifies to $0.3$ .

The problem says "when 30% of a number is added to the number, the result is 143." We can write this as an equation: $x + 0.3x = 143$ .
This equation perfectly captures the problem's information!

We've got $x + 0.3x$ .
Remember that $x$ is the same as $1 \cdot x$ , so $x + 0.3x$ is the same as $1x + 0.3x = 1.3x$ .
So, our equation becomes $1.3x = 143$ .

The number is $\boxed{110}$ .