Linear Equations and Applications

The sum of three consecutive odd numbers is 69.  The equation to determine the numbers is shown below.
n + (n + 2) + (n + 4) = 69
What is the third odd number?

• 21
• 23
• 25
• 73

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A linear equation is shown below.
2(x + 3) - 4 = 18
Which value of x makes the equation true?

• x = 3
• x = 6
• x = 11
• x = 8 

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A gadget is $4 less than three times another.  The total for the two items is $80.
How much are the two items?
x + (3x - 4) = 80

• $40 and $40
• $21 and $59
• $30 and $50
• $27 and $53

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Sarah has $14 and earns $6.25 per hour at work.  
Which equation can be used to determine how much money, m, Sarah has after working any number of hours, h?

• m = 14h + 6.25
• m = 6.25h + 14
• 14 = m + 6.25h
• 6.25 = 14m + h

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Julius has $22 and earns $8.50 per hour at work.  The equation to determine how much money, m, Julius has after working h hours is given below.
m = 8.5h + 22
How long will it take Julius to earn $124.00?

• 10 hours
• 11 hours
• 12 hours
• 13 hours

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A real estate agent earns a base salary of $1250.  For every house, h, she sells, she receives $750.  
Which equation could be used to determine the amount of money, m, she would have after selling any number of houses, h?

• m = 1250 + 750h
• m = 750 + 1250h
• 1250 = 750h + m
• 750 = 1250m + h

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Brandon earns $1050, plus an additional $825 for each house he sells.
m = 1050 + 825h 
can be used to represent this scenario.
How much money will he have if he sells 7 houses?

• $1,882
• $13,125
• $8,175
• $6,825

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At the theater, Fred purchased x popcorns and y drinks.  He spent a total of $25.  The equation below represents this scenario.
4x + 3y = 25
What does the solution (4, 3) represent?

• Popcorn costs $4 each and drinks cost $4 each
• Fred purchased 4 popcorns and 3 drinks
• Fred spent $4 on popcorn and $3 on drinks
• Fred purchased 3 popcorns and 4 drinks

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A pizza shop charges $12 per pizza and a delivery fee of $4.
Which equation represents the cost, c, for any number of pizzas, p?

• c = 4p + 12
• c = 12p + 4
• c = 16p
• p = 12 + 4 + c

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A service center charges a flat fee of $25, plus $45 per hour to repair cars.  
y = 45x + 25
George gets his car repaired and it takes 2.5 hours.
What is the total cost of his repair?

• $72.50
• $175.00
• $107.50
• $137.50

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