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Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 miles per hour. The other car leaves at 4:00 p.m. traveling at an average rate of 75 miles per hour. Let  x represent the number of hours after the first car leaves.

How many hours after the first car leaves will the two cars be 380 miles apart?


Enter an equation that can be used to solve this problem

Solve for  x and enter the number of hours

 

 

Which inequality models this problem?

 

Jason started a hat-making business. He spent $750 to purchase supplies to get started and he uses about $3.50 worth of supplies per hat made. Jason charges $15 for each hat. Let  h represent the number of hats.

What is the minimum number of hats Jason will need to sell to make a profit?

 

-15h<750+3.5h

-15h>750+3.5h

-3.5h≥750+15h

-3.5h>750+15h

 

The formula for the average of two numbers is  m= a+b/2

Solve for  a.

 

 

A photographer offers a photo shoot for a $85 flat fee. Customers may purchase prints for $5 per sheet.

How many sheets can a customer purchase and spend at most $150?

What linear inequality with variable x represents this situation?

What is the solution to that inequality? Enter the solution as an inequality using  x.

Guest Sep 25, 2017
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2+0 Answers

 #1
avatar+79786 
+1

Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 miles per hour. The other car leaves at 4:00 p.m. traveling at an average rate of 75 miles per hour. Let  x represent the number of hours after the first car leaves.

How many hours after the first car leaves will the two cars be 380 miles apart?

 

 

We want to find this : distance traveled by first car  + distance traveled  bt second car  = 380

And distance  = rate * time

 

So...the first car travels x hours and the second car travels one hour less = x - 1

And we have

 

55x + 75(x - 1)  = 380     simplify

 

55x  +  75x - 75  = 380   add 75 to both sides

 

130x  =  455     divide both sides by 130

 

x = 3.5 hrs

 

Jason started a hat-making business. He spent $750 to purchase supplies to get started and he uses about $3.50 worth of supplies per hat made. Jason charges $15 for each hat. Let  h represent the number of hats.

What is the minimum number of hats Jason will need to sell to make a profit?

 

He will make a profit when Sales > Costs  ...so

 

15h   >  750  + 3.50h         subtract   3.50h from both sides

 

11.5h > 750      divide both sides by  11.5

 

h > ≈  66 hats

 

 

 

m  =   [ a + b] / 2   multiply both sides by 2

 

2m  = a + b       subtract b from both sides

 

2m - b  = a

 

That's all I have time for....!!!!

 

 

cool cool cool

CPhill  Sep 25, 2017
 #2
avatar+79786 
+1

Last one :

 

A photographer offers a photo shoot for a $85 flat fee. Customers may purchase prints for $5 per sheet.

How many sheets can a customer purchase and spend at most $150?

What linear inequality with variable x represents this situation?

What is the solution to that inequality? Enter the solution as an inequality using  x.

 

 

For the first one....we have this inequality

 

85 + 5x ≤  150         where x is the number of sheets

Subtract 85  from both sides

5x ≤ 65

Divide both sides  by 5

x ≤ 13     .....so the customer can by 13 sheets at most

 

 

cool cool cool

CPhill  Sep 25, 2017

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