Math / Numbers & Operations

QuestionSolve Problems with Percent - Quiz - Level F
After a storm damages the community center, Shanika and her friends hold fundrais events to help pay for repairs. After the first event, they raise $\$ 240$ , which is $10 \%$ of total amount that they want to raise.
What is the total amount of money that Shanika and her friends want to raise?

Studdy Solution

STEP 1

What is this asking? Shanika and her friends raised $\$240$ , which is $10\%$ of their goal.
How much money do they want to raise in total? Watch out! Don't mix up the part ( $\$240$ ) with the whole (the total amount they want to raise).

STEP 2

1. Set up the percentage equation.
2. Solve for the total amount.

STEP 3

We know that $\$240$ is $10\%$ of the total amount.
Let's use $T$ to represent the total amount they want to raise.

STEP 4

We can write this as an equation: $10\%$ of $T$ is equal to $\$240$ .
Remember, "of" means multiply, and " $\%$ " means "per hundred" or "divided by 100".

STEP 5

So, our equation looks like this: $\frac{10}{100} \cdot T = 240$

STEP 6

Goal: Get $T$ by itself!
To do this, we need to divide both sides of the equation by $\frac{10}{100}$ .
Dividing by a fraction is the same as multiplying by its reciprocal (flip it!). The reciprocal of $\frac{10}{100}$ is $\frac{100}{10}$ .

STEP 7

So, let's multiply both sides of the equation by $\frac{100}{10}$ : $\frac{100}{10} \cdot \frac{10}{100} \cdot T = 240 \cdot \frac{100}{10}$

STEP 8

On the left side, $\frac{100}{10} \cdot \frac{10}{100}$ simplifies to $1$ (we're dividing to one!), leaving us with just $T$ .
Awesome!

STEP 9

On the right side, we have $240 \cdot \frac{100}{10}$ .
We can simplify $\frac{100}{10}$ to $10$ .
So, we have $240 \cdot 10$ .

STEP 10

Now, we calculate $240 \cdot 10 = 2400$ .

STEP 11

So, $T = 2400$ .
This means the total amount Shanika and her friends want to raise is $\$2400$ !

STEP 12

Shanika and her friends want to raise a total of $\$2400$ .

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Studdy Solution

STEP 1

What is this asking? Shanika and her friends raised $\$240$ , which is $10\%$ of their goal.
How much money do they want to raise in total? Watch out! Don't mix up the part ( $\$240$ ) with the whole (the total amount they want to raise).

STEP 2

1. Set up the percentage equation.
2. Solve for the total amount.

STEP 3

We know that $\$240$ is $10\%$ of the total amount.
Let's use $T$ to represent the total amount they want to raise.

STEP 4

We can write this as an equation: $10\%$ of $T$ is equal to $\$240$ .
Remember, "of" means multiply, and " $\%$ " means "per hundred" or "divided by 100".

STEP 5

So, our equation looks like this: $\frac{10}{100} \cdot T = 240$

STEP 6

Goal: Get $T$ by itself!
To do this, we need to divide both sides of the equation by $\frac{10}{100}$ .
Dividing by a fraction is the same as multiplying by its reciprocal (flip it!). The reciprocal of $\frac{10}{100}$ is $\frac{100}{10}$ .

STEP 7

So, let's multiply both sides of the equation by $\frac{100}{10}$ : $\frac{100}{10} \cdot \frac{10}{100} \cdot T = 240 \cdot \frac{100}{10}$

STEP 8

On the left side, $\frac{100}{10} \cdot \frac{10}{100}$ simplifies to $1$ (we're dividing to one!), leaving us with just $T$ .
Awesome!

STEP 9

On the right side, we have $240 \cdot \frac{100}{10}$ .
We can simplify $\frac{100}{10}$ to $10$ .
So, we have $240 \cdot 10$ .

STEP 10

Now, we calculate $240 \cdot 10 = 2400$ .

STEP 11

So, $T = 2400$ .
This means the total amount Shanika and her friends want to raise is $\$2400$ !

STEP 12

Shanika and her friends want to raise a total of $\$2400$ .

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Studdy Solution

STEP 1

What is this asking? Shanika and her friends raised $240\$240$240, which is 10%10\%10% of their goal.How much money do they want to raise in total? Watch out! Don't mix up the part ($240\$240$240) with the whole (the total amount they want to raise).

STEP 2

1. Set up the percentage equation.2. Solve for the total amount.

STEP 3

We know that $240\$240$240 is 10%10\%10% of the total amount.Let's use TTT to represent the **total amount** they want to raise.

STEP 4

We can write this as an equation: 10%10\%10% of TTT is equal to $240\$240$240.Remember, "of" means multiply, and "%\%%" means "per hundred" or "divided by 100".

STEP 5

So, our equation looks like this: 10100⋅T=240 \frac{10}{100} \cdot T = 240 10010​⋅T=240

STEP 6

**Goal:** Get TTT by itself!To do this, we need to divide both sides of the equation by 10100\frac{10}{100}10010​.Dividing by a fraction is the same as multiplying by its reciprocal (flip it!). The reciprocal of 10100\frac{10}{100}10010​ is 10010\frac{100}{10}10100​.

STEP 7

So, let's multiply both sides of the equation by 10010\frac{100}{10}10100​: 10010⋅10100⋅T=240⋅10010 \frac{100}{10} \cdot \frac{10}{100} \cdot T = 240 \cdot \frac{100}{10} 10100​⋅10010​⋅T=240⋅10100​

STEP 8

On the left side, 10010⋅10100\frac{100}{10} \cdot \frac{10}{100}10100​⋅10010​ simplifies to 111 (we're dividing to one!), leaving us with just TTT.Awesome!

STEP 9

On the right side, we have 240⋅10010240 \cdot \frac{100}{10}240⋅10100​.We can simplify 10010\frac{100}{10}10100​ to 101010.So, we have 240⋅10240 \cdot 10240⋅10.

STEP 10

Now, we calculate 240⋅10=2400240 \cdot 10 = 2400240⋅10=2400.

STEP 11

So, T=2400T = 2400T=2400.This means the **total amount** Shanika and her friends want to raise is $2400\$2400$2400!

STEP 12

Shanika and her friends want to raise a total of $2400\$2400$2400.

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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.

What is this asking? Shanika and her friends raised $\$240$ , which is $10\%$ of their goal.
How much money do they want to raise in total? Watch out! Don't mix up the part ( $\$240$ ) with the whole (the total amount they want to raise).

1. Set up the percentage equation.
2. Solve for the total amount.

We know that $\$240$ is $10\%$ of the total amount.
Let's use $T$ to represent the total amount they want to raise.

We can write this as an equation: $10\%$ of $T$ is equal to $\$240$ .
Remember, "of" means multiply, and " $\%$ " means "per hundred" or "divided by 100".

So, our equation looks like this: $\frac{10}{100} \cdot T = 240$

Goal: Get $T$ by itself!
To do this, we need to divide both sides of the equation by $\frac{10}{100}$ .
Dividing by a fraction is the same as multiplying by its reciprocal (flip it!). The reciprocal of $\frac{10}{100}$ is $\frac{100}{10}$ .

So, let's multiply both sides of the equation by $\frac{100}{10}$ : $\frac{100}{10} \cdot \frac{10}{100} \cdot T = 240 \cdot \frac{100}{10}$

On the left side, $\frac{100}{10} \cdot \frac{10}{100}$ simplifies to $1$ (we're dividing to one!), leaving us with just $T$ .
Awesome!

On the right side, we have $240 \cdot \frac{100}{10}$ .
We can simplify $\frac{100}{10}$ to $10$ .
So, we have $240 \cdot 10$ .

Now, we calculate $240 \cdot 10 = 2400$ .

So, $T = 2400$ .
This means the total amount Shanika and her friends want to raise is $\$2400$ !

Shanika and her friends want to raise a total of $\$2400$ .