Math / Algebra

QuestionQuestion 10 (3 points)
4. A coffee shop sells pastries for $\$ 3$ each. The following aquation modelas the total revenue for the day $f(x)$ (if dollary) from solling $x$ pastries. Round all answers to the nearest hundredth, if necessary. $1(x)=3 x-20$ b. How many pastries would need to be sold to make $\$ 436$ revenue? (3 points) $\square$ $\square$

Studdy Solution

STEP 1

1. The coffee shop sells each pastry for \$3.
2. The function $ f(x) = 3x - 20 $ models the total revenue in dollars from selling $ x $ pastries.
3. We need to find the number of pastries $ x $ that need to be sold to make \$436 in revenue.
4. Answers should be rounded to the nearest hundredth if necessary.

STEP 2

1. Understand the given function.
2. Set up the equation to find $x$ .
3. Solve the equation for $x$ .
4. Round the answer to the nearest hundredth if necessary.

STEP 3

Understand the given function $f(x) = 3x - 20$ .
This function represents the total revenue from selling $x$ pastries, where each pastry contributes \$3 to the revenue, and there is a constant subtraction of \$20.

STEP 4

Set up the equation to find $x$ .
We want the revenue to be \$436, so set $ f(x) = 436 $.
$3x - 20 = 436$

STEP 5

Solve the equation for $x$ .
First, add 20 to both sides of the equation to isolate the term with $x$ :
$3x - 20 + 20 = 436 + 20$ $3x = 456$
Next, divide both sides by 3 to solve for $x$ :
$x = \frac{456}{3}$ $x = 152$

STEP 6

Round the answer to the nearest hundredth if necessary.
Since $x = 152$ is already a whole number, no rounding is necessary.
The number of pastries that need to be sold to make \$436 in revenue is:
$\boxed{152}$

Was this helpful?

Studdy Solution

STEP 1

STEP 2

1. Understand the given function.
2. Set up the equation to find $x$ .
3. Solve the equation for $x$ .
4. Round the answer to the nearest hundredth if necessary.

STEP 3

Understand the given function $f(x) = 3x - 20$ .
This function represents the total revenue from selling $x$ pastries, where each pastry contributes \$3 to the revenue, and there is a constant subtraction of \$20.

STEP 4

Set up the equation to find $x$ .
We want the revenue to be \$436, so set \( f(x) = 436 \).
$3x - 20 = 436$

STEP 5

Solve the equation for $x$ .
First, add 20 to both sides of the equation to isolate the term with $x$ :
$3x - 20 + 20 = 436 + 20$ $3x = 456$
Next, divide both sides by 3 to solve for $x$ :
$x = \frac{456}{3}$ $x = 152$

STEP 6

Round the answer to the nearest hundredth if necessary.
Since $x = 152$ is already a whole number, no rounding is necessary.
The number of pastries that need to be sold to make \$436 in revenue is:
$\boxed{152}$

Get Studdy

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.

Studdy Solution

STEP 1

STEP 2

1. Understand the given function.2. Set up the equation to find x x x.3. Solve the equation for x x x.4. Round the answer to the nearest hundredth if necessary.

STEP 3

Understand the given function f(x)=3x−20 f(x) = 3x - 20 f(x)=3x−20.This function represents the total revenue from selling x x x pastries, where each pastry contributes \$3 to the revenue, and there is a constant subtraction of \$20.

STEP 4

Set up the equation to find x x x.We want the revenue to be \$436, so set \( f(x) = 436 \).3x−20=436 3x - 20 = 436 3x−20=436

STEP 5

Solve the equation for x x x.First, add 20 to both sides of the equation to isolate the term with x x x:3x−20+20=436+20 3x - 20 + 20 = 436 + 20 3x−20+20=436+20 3x=456 3x = 456 3x=456Next, divide both sides by 3 to solve for x x x:x=4563 x = \frac{456}{3} x=3456​ x=152 x = 152 x=152

STEP 6

Round the answer to the nearest hundredth if necessary.Since x=152 x = 152 x=152 is already a whole number, no rounding is necessary.The number of pastries that need to be sold to make \$436 in revenue is:152 \boxed{152} 152​

Get Studdy

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.

1. Understand the given function.
2. Set up the equation to find $x$ .
3. Solve the equation for $x$ .
4. Round the answer to the nearest hundredth if necessary.

Understand the given function $f(x) = 3x - 20$ .
This function represents the total revenue from selling $x$ pastries, where each pastry contributes \$3 to the revenue, and there is a constant subtraction of \$20.

Set up the equation to find $x$ .
We want the revenue to be \$436, so set \( f(x) = 436 \).
$3x - 20 = 436$

Solve the equation for $x$ .
First, add 20 to both sides of the equation to isolate the term with $x$ :
$3x - 20 + 20 = 436 + 20$ $3x = 456$
Next, divide both sides by 3 to solve for $x$ :
$x = \frac{456}{3}$ $x = 152$

Round the answer to the nearest hundredth if necessary.
Since $x = 152$ is already a whole number, no rounding is necessary.
The number of pastries that need to be sold to make \$436 in revenue is:
$\boxed{152}$