Math / Algebra

Question7. To serve 1 person at a local restaurant, it takes 10 minutes. To serve 5 people, it takes 18 minutes. Write and solve an equation to find the number of minutes it will take to serve a party of 8 .
Equation: Solution:

Studdy Solution

STEP 1

1. Serving time for 1 person is 10 minutes.
2. Serving time for 5 people is 18 minutes.
3. We need to find the serving time for 8 people.
4. The relationship between the number of people and the time taken is linear.

STEP 2

1. Identify the linear relationship.
2. Define variables and write an equation.
3. Solve the equation for the desired number of people.

STEP 3

Identify the linear relationship.
Assume that the time taken to serve people can be expressed as a linear equation of the form $T = m \cdot P + c$ , where $T$ is the total time, $P$ is the number of people, $m$ is the rate of increase in time per person, and $c$ is a constant.

STEP 4

Define variables and write an equation.
We have two data points: - For 1 person, $T = 10$ minutes. - For 5 people, $T = 18$ minutes.
Using these points, we can set up two equations:
1. $10 = m \cdot 1 + c$
2. $18 = m \cdot 5 + c$
Solve these equations to find $m$ and $c$ .

STEP 5

Subtract the first equation from the second to eliminate $c$ :
$18 - 10 = 5m + c - (m + c)$ $8 = 4m$ $m = 2$
Substitute $m = 2$ back into the first equation to find $c$ :
$10 = 2 \cdot 1 + c$ $10 = 2 + c$ $c = 8$
The equation is $T = 2P + 8$ .

STEP 6

Solve the equation for the desired number of people.
Substitute $P = 8$ into the equation:
$T = 2 \cdot 8 + 8$ $T = 16 + 8$ $T = 24$
The number of minutes it will take to serve a party of 8 is:
$\boxed{24}$

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Question7. To serve 1 person at a local restaurant, it takes 10 minutes. To serve 5 people, it takes 18 minutes. Write and solve an equation to find the number of minutes it will take to serve a party of 8 .
Equation: Solution:

Studdy Solution

STEP 1

1. Serving time for 1 person is 10 minutes.
2. Serving time for 5 people is 18 minutes.
3. We need to find the serving time for 8 people.
4. The relationship between the number of people and the time taken is linear.

STEP 2

1. Identify the linear relationship.
2. Define variables and write an equation.
3. Solve the equation for the desired number of people.

STEP 3

Identify the linear relationship.
Assume that the time taken to serve people can be expressed as a linear equation of the form $T = m \cdot P + c$ , where $T$ is the total time, $P$ is the number of people, $m$ is the rate of increase in time per person, and $c$ is a constant.

STEP 4

Define variables and write an equation.
We have two data points: - For 1 person, $T = 10$ minutes. - For 5 people, $T = 18$ minutes.
Using these points, we can set up two equations:
1. $10 = m \cdot 1 + c$
2. $18 = m \cdot 5 + c$
Solve these equations to find $m$ and $c$ .

STEP 5

Subtract the first equation from the second to eliminate $c$ :
$18 - 10 = 5m + c - (m + c)$ $8 = 4m$ $m = 2$
Substitute $m = 2$ back into the first equation to find $c$ :
$10 = 2 \cdot 1 + c$ $10 = 2 + c$ $c = 8$
The equation is $T = 2P + 8$ .

STEP 6

Solve the equation for the desired number of people.
Substitute $P = 8$ into the equation:
$T = 2 \cdot 8 + 8$ $T = 16 + 8$ $T = 24$
The number of minutes it will take to serve a party of 8 is:
$\boxed{24}$

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Question7. To serve 1 person at a local restaurant, it takes 10 minutes. To serve 5 people, it takes 18 minutes. Write and solve an equation to find the number of minutes it will take to serve a party of 8 .Equation: Solution:

Studdy Solution

STEP 1

1. Serving time for 1 person is 10 minutes.2. Serving time for 5 people is 18 minutes.3. We need to find the serving time for 8 people.4. The relationship between the number of people and the time taken is linear.

STEP 2

1. Identify the linear relationship.2. Define variables and write an equation.3. Solve the equation for the desired number of people.

STEP 3

STEP 4

STEP 5

STEP 6

Solve the equation for the desired number of people.Substitute P=8 P = 8 P=8 into the equation:T=2⋅8+8 T = 2 \cdot 8 + 8 T=2⋅8+8 T=16+8 T = 16 + 8 T=16+8 T=24 T = 24 T=24The number of minutes it will take to serve a party of 8 is:24 \boxed{24} 24​

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.

Question7. To serve 1 person at a local restaurant, it takes 10 minutes. To serve 5 people, it takes 18 minutes. Write and solve an equation to find the number of minutes it will take to serve a party of 8 .
Equation: Solution:

1. Serving time for 1 person is 10 minutes.
2. Serving time for 5 people is 18 minutes.
3. We need to find the serving time for 8 people.
4. The relationship between the number of people and the time taken is linear.

1. Identify the linear relationship.
2. Define variables and write an equation.
3. Solve the equation for the desired number of people.

Solve the equation for the desired number of people.
Substitute $P = 8$ into the equation:
$T = 2 \cdot 8 + 8$ $T = 16 + 8$ $T = 24$
The number of minutes it will take to serve a party of 8 is:
$\boxed{24}$