Math / Algebra

Question- A factory manager, Vin Diesel, knows that on any given day, n employees can fill $p(n)=2 n-8$ orders.
1. How many orders can 10 employees fill in a $\cdot$ day? WARM-UP 2.On Monday, 120 orders need to be filled. How many employees are needed on Monday? 3.On Tuesday, 64 orders need to be filled. How many employees are needed on Tuesday?

Studdy Solution

STEP 1

1. The given function for the number of orders filled by $n$ employees is $p(n) = 2n - 8$ .
2. To determine the number of orders filled by a given number of employees, substitute the number of employees into the function $p(n)$ .
3. To determine the number of employees needed to fill a given number of orders, solve for $n$ in the equation $p(n) = 2n - 8$ .

STEP 2

1. Calculate the number of orders filled by 10 employees.
2. Determine the number of employees needed to fill 120 orders.
3. Determine the number of employees needed to fill 64 orders.

STEP 3

To find the number of orders 10 employees can fill, substitute $n = 10$ into the function $p(n)$ .
$p(10) = 2 \cdot 10 - 8$

STEP 4

Simplify the expression:
$p(10) = 20 - 8 = 12$

STEP 5

To find the number of employees needed to fill 120 orders, set $p(n) = 120$ and solve for $n$ .
$120 = 2n - 8$

STEP 6

Add 8 to both sides of the equation to isolate the term with $n$ .
$120 + 8 = 2n$

STEP 7

Simplify the left side:
$128 = 2n$

STEP 8

Divide both sides by 2 to solve for $n$ .
$n = \frac{128}{2} = 64$

STEP 9

To find the number of employees needed to fill 64 orders, set $p(n) = 64$ and solve for $n$ .
$64 = 2n - 8$

STEP 10

Add 8 to both sides of the equation to isolate the term with $n$ .
$64 + 8 = 2n$

STEP 11

Simplify the left side:
$72 = 2n$

STEP 12

Divide both sides by 2 to solve for $n$ .
$n = \frac{72}{2} = 36$
Solution:
1. 10 employees can fill 12 orders in a day.
2. 120 orders need 64 employees on Monday.
3. 64 orders need 36 employees on Tuesday.

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Studdy Solution

STEP 1

STEP 2

1. Calculate the number of orders filled by 10 employees.
2. Determine the number of employees needed to fill 120 orders.
3. Determine the number of employees needed to fill 64 orders.

STEP 3

To find the number of orders 10 employees can fill, substitute $n = 10$ into the function $p(n)$ .
$p(10) = 2 \cdot 10 - 8$

STEP 4

Simplify the expression:
$p(10) = 20 - 8 = 12$

STEP 5

To find the number of employees needed to fill 120 orders, set $p(n) = 120$ and solve for $n$ .
$120 = 2n - 8$

STEP 6

Add 8 to both sides of the equation to isolate the term with $n$ .
$120 + 8 = 2n$

STEP 7

Simplify the left side:
$128 = 2n$

STEP 8

Divide both sides by 2 to solve for $n$ .
$n = \frac{128}{2} = 64$

STEP 9

To find the number of employees needed to fill 64 orders, set $p(n) = 64$ and solve for $n$ .
$64 = 2n - 8$

STEP 10

Add 8 to both sides of the equation to isolate the term with $n$ .
$64 + 8 = 2n$

STEP 11

Simplify the left side:
$72 = 2n$

STEP 12

Divide both sides by 2 to solve for $n$ .
$n = \frac{72}{2} = 36$
Solution:
1. 10 employees can fill 12 orders in a day.
2. 120 orders need 64 employees on Monday.
3. 64 orders need 36 employees on Tuesday.

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Studdy Solution

STEP 1

STEP 2

1. Calculate the number of orders filled by 10 employees.2. Determine the number of employees needed to fill 120 orders.3. Determine the number of employees needed to fill 64 orders.

STEP 3

To find the number of orders 10 employees can fill, substitute n=10n = 10n=10 into the function p(n)p(n)p(n).p(10)=2⋅10−8 p(10) = 2 \cdot 10 - 8 p(10)=2⋅10−8

STEP 4

Simplify the expression:p(10)=20−8=12 p(10) = 20 - 8 = 12 p(10)=20−8=12

STEP 5

To find the number of employees needed to fill 120 orders, set p(n)=120p(n) = 120p(n)=120 and solve for nnn.120=2n−8 120 = 2n - 8 120=2n−8

STEP 6

Add 8 to both sides of the equation to isolate the term with nnn.120+8=2n 120 + 8 = 2n 120+8=2n

STEP 7

Simplify the left side:128=2n 128 = 2n 128=2n

STEP 8

Divide both sides by 2 to solve for nnn.n=1282=64 n = \frac{128}{2} = 64 n=2128​=64

STEP 9

To find the number of employees needed to fill 64 orders, set p(n)=64p(n) = 64p(n)=64 and solve for nnn.64=2n−8 64 = 2n - 8 64=2n−8

STEP 10

Add 8 to both sides of the equation to isolate the term with nnn.64+8=2n 64 + 8 = 2n 64+8=2n

STEP 11

Simplify the left side:72=2n 72 = 2n 72=2n

STEP 12

Divide both sides by 2 to solve for nnn.n=722=36 n = \frac{72}{2} = 36 n=272​=36Solution:1. 10 employees can fill 12 orders in a day.2. 120 orders need 64 employees on Monday.3. 64 orders need 36 employees on Tuesday.

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1. Calculate the number of orders filled by 10 employees.
2. Determine the number of employees needed to fill 120 orders.
3. Determine the number of employees needed to fill 64 orders.

To find the number of orders 10 employees can fill, substitute $n = 10$ into the function $p(n)$ .
$p(10) = 2 \cdot 10 - 8$

Simplify the expression:
$p(10) = 20 - 8 = 12$

To find the number of employees needed to fill 120 orders, set $p(n) = 120$ and solve for $n$ .
$120 = 2n - 8$

Add 8 to both sides of the equation to isolate the term with $n$ .
$120 + 8 = 2n$

Simplify the left side:
$128 = 2n$

Divide both sides by 2 to solve for $n$ .
$n = \frac{128}{2} = 64$

To find the number of employees needed to fill 64 orders, set $p(n) = 64$ and solve for $n$ .
$64 = 2n - 8$

Add 8 to both sides of the equation to isolate the term with $n$ .
$64 + 8 = 2n$

Simplify the left side:
$72 = 2n$

Divide both sides by 2 to solve for $n$ .
$n = \frac{72}{2} = 36$
Solution:
1. 10 employees can fill 12 orders in a day.
2. 120 orders need 64 employees on Monday.
3. 64 orders need 36 employees on Tuesday.