Question Find the number Riley thought of, given that when tripled and subtracted by 5, the result is 7.

Studdy Solution

STEP 1

Assumptions
1. Riley thinks of an unknown number, which we will denote as $f$ .
2. Riley triples the number ( $3f$ ).
3. Riley then subtracts 5 from the tripled number ( $3f - 5$ ).
4. The result after subtracting 5 is given as 7.

STEP 2

To write an equation that describes the situation, we represent the operations Riley performs on the number $f$ as an algebraic expression.
$3f - 5 = 7$

STEP 3

Now, we will solve the equation for $f$ to find the number Riley thinks of. First, we need to isolate the term with $f$ on one side of the equation. We can do this by adding 5 to both sides of the equation to cancel out the -5.
$3f - 5 + 5 = 7 + 5$

STEP 4

Simplify both sides of the equation.
$3f = 12$

STEP 5

To find the value of $f$ , we now divide both sides of the equation by 3.
$\frac{3f}{3} = \frac{12}{3}$

STEP 6

Simplify the equation to solve for $f$ .
$f = 4$
Riley's number, $f$ , is 4.

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Question Find the number Riley thought of, given that when tripled and subtracted by 5, the result is 7.

Studdy Solution

STEP 1

Assumptions
1. Riley thinks of an unknown number, which we will denote as $f$ .
2. Riley triples the number ( $3f$ ).
3. Riley then subtracts 5 from the tripled number ( $3f - 5$ ).
4. The result after subtracting 5 is given as 7.

STEP 2

To write an equation that describes the situation, we represent the operations Riley performs on the number $f$ as an algebraic expression.
$3f - 5 = 7$

STEP 3

Now, we will solve the equation for $f$ to find the number Riley thinks of. First, we need to isolate the term with $f$ on one side of the equation. We can do this by adding 5 to both sides of the equation to cancel out the -5.
$3f - 5 + 5 = 7 + 5$

STEP 4

Simplify both sides of the equation.
$3f = 12$

STEP 5

To find the value of $f$ , we now divide both sides of the equation by 3.
$\frac{3f}{3} = \frac{12}{3}$

STEP 6

Simplify the equation to solve for $f$ .
$f = 4$
Riley's number, $f$ , is 4.

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Question Find the number Riley thought of, given that when tripled and subtracted by 5, the result is 7.

Studdy Solution

STEP 1

Assumptions1. Riley thinks of an unknown number, which we will denote as fff.2. Riley triples the number (3f3f3f).3. Riley then subtracts 5 from the tripled number (3f−53f - 53f−5).4. The result after subtracting 5 is given as 7.

STEP 2

To write an equation that describes the situation, we represent the operations Riley performs on the number fff as an algebraic expression.3f−5=73f - 5 = 73f−5=7

STEP 3

Now, we will solve the equation for fff to find the number Riley thinks of. First, we need to isolate the term with fff on one side of the equation. We can do this by adding 5 to both sides of the equation to cancel out the -5.3f−5+5=7+53f - 5 + 5 = 7 + 53f−5+5=7+5

STEP 4

Simplify both sides of the equation.3f=123f = 123f=12

STEP 5

To find the value of fff, we now divide both sides of the equation by 3.3f3=123\frac{3f}{3} = \frac{12}{3}33f​=312​

STEP 6

Simplify the equation to solve for fff.f=4f = 4f=4Riley's number, fff, is 4.

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Assumptions
1. Riley thinks of an unknown number, which we will denote as $f$ .
2. Riley triples the number ( $3f$ ).
3. Riley then subtracts 5 from the tripled number ( $3f - 5$ ).
4. The result after subtracting 5 is given as 7.

To write an equation that describes the situation, we represent the operations Riley performs on the number $f$ as an algebraic expression.
$3f - 5 = 7$

Now, we will solve the equation for $f$ to find the number Riley thinks of. First, we need to isolate the term with $f$ on one side of the equation. We can do this by adding 5 to both sides of the equation to cancel out the -5.
$3f - 5 + 5 = 7 + 5$

Simplify both sides of the equation.
$3f = 12$

To find the value of $f$ , we now divide both sides of the equation by 3.
$\frac{3f}{3} = \frac{12}{3}$

Simplify the equation to solve for $f$ .
$f = 4$
Riley's number, $f$ , is 4.