Creating and Solving Equations

15 more than x is 38

• x+15=38

• x-15=38

• x+38=15

• x-38=15

A gymnastics center charges a $60 registration fee and $15 per class. Olivia registers to take a class and pays a total of $210. Which equation can be used to determine how many classes Olivia signed up for?  

• 60 - 15x = 210 
• 15x - 60 = 210
• 15x + 60 = 210 
• 210 + 15x = 60 

Renting boats on a lake costs $22 per hour plus a flat fee of $10 for insurance. If you paid $98 to rent the boat, how many hours did you rent the boat?
What is the correct equation to solve?

• 22 + 10h = 98
• 22 + 10 = 98h
• 98 + 10 = 22h
• 22h + 10 = 98

x/9=28

• 9 times a number is 28
• A number multiplied by 9 equals 28
• A number removed from 9 is 28
• The quotient of 9 and a number is 28

120 more than twice a number is the same as halve a number removed from 8

• 2t+120= ^t/₂ - 8

• 120+2t = ^t/₂ - 8

• 2t+120 = 8 - ^t/₂

• 2(t+120)=8 - ^t/₂

4 times a number increased by 5 is the same as 3 times the difference of a number and 2.  Which of the following equations would find the number?

• 4n + 5 = 3n - 2
• 4n + 5 = 3(n - 2)
• 4n+5 = 3(n + 2)
• 4n + 5 = 3 - 2n

Taxi company A charges $8.00 to get into the cab and $0.75 per mile. Taxi company B charges $6.00 to get into a cab and $1.25 per mile. How many miles would the cost be the same for both companies? 

• 2 miles 
• 4 miles
• .50 mile
• -4 miles 

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

• 15x + 2.5 = 10x + 3

• 15 - 2.5x = 10 - 3x

• 15 + 2.5x = 10 + 3x

• 15 - 10 = 2.5x + 3x

If ChipCo sold their bags of corn chips for $5 per bag plus $1 for bagging it and it costs the same as $4 per bag of CrunchyChips corn chips plus their price of $2 for bagging it, what would the equation be and how many bags of chips would make them cost the same?

• 5 + 1x = 2x + 4; 1 bag of chips

• 9x = 3; 3 bags of chips

• 5x + 1 = 4x + 2; 1 bag of chips

• 5x = 6x; -1 bag of chips

Rachel and Sharon are splitting up their Pokemon cards.  Rachel has 4 fewer than 3 times as many as Sharon.  Together they have 100 cards.  Which equation could be used to solve for how many cards Sharon had originally?

• n + (3n - 4) = 100
• n - (3n - 4) = 100
• n + (4 - 3n) = 100
• 4 - 3n = 100