Solved Examples and Worksheet for Writing Linear Equations for the Situations

Q1Tim buys one goldfish and 4 guppies for a total cost of $18. Identify the equation representing this situation if f is the cost of a goldfish and g is the cost of a guppy.
A. 4f + g = 18
B. f + 4g = 18
C. f × 4g = 18
D. f - 4g = 18

Solutions
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Step: 1
Tim buys one goldfish and 4 guppies for a total cost of $18.
Step: 2
f + 4g = 18 is the required equation.
Correct Answer is :   f + 4g = 18
Q2A waiter earned $64 for 8 hours of work, including $28 in tips. Which equation helps you to find his hourly wage?

A. w = 64(8)
B. 28w - 64 = 8
C. 8(64) - 28 = w
D. 8w + 28 = 64

Solutions
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Step: 1
Total amount earned by the waiter for 8 hours of work = $64.
Step: 2
Tips amount for 8 hours of work = $28.
Step: 3
Therefore, the equation that can be used to determine his hourly wage is 8w + 28 = 64.
Correct Answer is :   8w + 28 = 64
Q3Hardy earns $9 per hour. Which of the following rules describes the relation between the number of hours he worked and the amount he earns?
A. Earnings = $9 / number of hours
B. Earnings = $9 x number of hours
C. Earnings = $9 + number of hours
D. Earnings = $9 - number of hours

Solutions
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Step: 1
As the number of working hours increase the amount he earns also increases at the rate of $9 / hr.
Step: 2
So, the number of hours he worked and the amount he earns is given by the relation,
Earnings = $9 x number of hours.
Correct Answer is :   Earnings = $9 x number of hours
Q4A soap manufacturing company packs the soap in cartons. Which of the following rules represents the relationship between the cartons and soap, if 137 bars soap are packed in one carton?
A. Number of bars of soap = 137 × Number of cartons
B. Number of bars of soap = 137 / Number of cartons
C. Number of bars of soap = 137 - Number of cartons
D. Number of bars of soap = 137 + Number of cartons

Solutions
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Step: 1
Number of bars of soap that fit in 1 carton = 137
Step: 2
As the number of cartons increase by 1, the number of bars of soap increase by 137.
Step: 3
So, the rule representing the relationship between the bars of soap and the cartons can be given as, Number of bars of soap = 137 × Number of cartons.
Correct Answer is :   Number of bars of soap = 137 × Number of cartons
Q5Jim buys a car worth $7265 on installment basis. He pays $1325 initially and $990 every month. Which equation best describes the situation?
A. (990 + 1325)n = 7265
B. 1325n + 990 = 7265
C. 990n + 1325 = 7265
D. 990 + n + 1325 = 7265

Solutions
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Step: 1
Let n be the number of months that Jim will take to repay the total amount.
Step: 2
Cost of the car = Initial payment + (Monthly installment x Number of months)
Step: 3
990n + 1325 = 7265
  [Substitute and rewrite.]
Correct Answer is :   990n + 1325 = 7265
Q6Bill buys a car worth $5,565. He makes a down payment of $1485 and makes a monthly payment of $510. How many months will it take him to pay the total amount?

A. 13
B. 8
C. 7
D. 12

Solutions
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Step: 1
Let n be the number of months taken to pay the total amount.
Step: 2
Cost of the car = Initial pay + (Monthly pay × Number of months)
Step: 3
5565 = 1485 + ( 510 × n )
  [Write an equation.]
Step: 4
5565 - 1485 = 1485 + 510n - 1485
  [Subtract 1485 from each side.]
Step: 5
4080 = 510n
  [Simplify.]
Step: 6
4080510 = 510n510
  [Divide each side by 510.]
Step: 7
8 = n
  [Simplify.]
Step: 8
It takes 8 months for Bill to pay the total amount.
Correct Answer is :   8
Q7Joe buys one goldfish and 4 guppies for a total cost of $10. What is the cost of the goldfish, if each guppy costs $2?
A. $2
B. $12
C. $1
D. $6

Solutions
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Step: 1
Let f be the cost of a goldfish and g be the cost of a guppy.
Step: 2
f + 4g = 10
  [Write the equation.]
Step: 3
f + 4 × 2 = 10
  [Replace the variables with the values, given.]
Step: 4
f + 8 = 10
  [Multiply.]
Step: 5
f + 8 - 8 = 10 - 8
  [Subtracting 8 from the two sides of the equation.]
Step: 6
f = 2
  [Simplify.]
Step: 7
The cost of the goldfish is $2.
Correct Answer is :   $2
Q8Justin has 10 pencils less than twice as many pencils as Jimmy. If Justin has 32 pencils, then how many pencils does Jimmy have?

A. 24 pencils
B. 19 pencils
C. 21 pencils
D. 23 pencils

Solutions
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Step: 1
Let Jimmy has m pencils.
Step: 2
Let Justin has p pencils.
Step: 3
p = 2 × m - 10
  [Write the equation.]
Step: 4
32 = 2m - 10
  [Substitute the values.]
Step: 5
2m - 10 = 32
  [Interchange L.H.S. and R.H.S.]
Step: 6
2m - 10 + 10 = 32 + 10
  [Add 10 to both sides of the equation.]
Step: 7
2m = 42
  [Simplify.]
Step: 8
2m2 = 422
  [Divide throughout by 2.]
Step: 9
m = 21
  [Simplify.]
Step: 10
Jimmy has 21 pencils.
Correct Answer is :   21 pencils
Q9The volume V of a prism is base area (B) times the height (h) of its prism. Which of the following equations best relates the variables?
A. V = Bh
B. V = B + h
C. V = Bh
D. V = hB

Solutions
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Step: 1
Volume of a prism = base area × height
  [Given.]
Step: 2
⇒ V = B × h; where V = volume, B = base area, and h = height
  [Substitute variables in step 1.]
Step: 3
Therefore, among the choices, V = Bh is the only equation that best relates the variables given.
Correct Answer is :   V = Bh
Q10The perimeter (P) of a regular pentagon is 5 times the length of a side (s). Which of the equations best relates the variables?
A. S = 5 + p
B. p = s5
C. p = 5s
D. p = 5S

Solutions
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Step: 1
Perimeter (P) of the pentagon varies directly with length of a side (s).
Step: 2
Therefore, P = 5s is the equation that best relates the variables.
Correct Answer is :   p = 5S
Q11The perimeter (P) of a quadrilateral is 4 times the length of a side (s). Which of the equations best relates the variables?

A. S = 4p
B. p = s4
C. p = 4S
D. p = 4s

Solutions
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Step: 1
Perimeter (P) of the quadrilateral varies directly with length of a side (s).
Step: 2
Therefore, P = 4s is the equation that best relates the variables.
Correct Answer is :    p = 4S
Q12A can of French onion soup weighs 118 grams. The weight of a box of n cans of the soup is W. Which of the following equations best relates the variables?
A. W + n = 118
B. W = n118
C. W = 118n
D. W = 118(n)

Solutions
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Step: 1
As the number of cans increase, the total weight of the box also increases.
Step: 2
Therefore, W = 118(n) best relates the variables.
Correct Answer is :   W = 118(n)
Q13Ed earns $p per hour working as a translator. He must work for h hours to earn $325. Which of the following equations best relates the variables?
A. hp = 325
B. h = p325
C. h = 325 + p
D. p = h325

Solutions
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Step: 1
Ed earns $p per hour.
Step: 2
To earn $325 he has to work for h hours.
Step: 3
If he works for 1 hour he earns $p, so if he works for h hours he earns $hp.
Step: 4
So, hp = 325.
Correct Answer is :   hp = 325
Q14Paul bought a few chocolates and cookies for 125 cents. Cost of a chocolate is 10 cents and that of a cookie is 15 cents. Identify an equation that models the cost of the chocolates and the cookies that Paul bought, if x represents the number of chocolates and y represents the number of cookies.
A. 15x - 10y = 125
B. 10x - 15y = 125
C. 15x + 10y = 125
D. 10x + 15y = 125

Solutions
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Step: 1
Cost of a chocolate = 10 cents
Step: 2
Cost of a cookie = 15 cents
Step: 3
(Cost of a chocolate × Number of chocolates) + (Cost of cookie × Number of cookies) = Total cost
  [Verbal model.]
Step: 4
10x + 15y = 125
  [Substitute the values.]
Step: 5
The equation that models the cost of the chocolates and cookies that Paul bought is 10x + 15y = 125.
Correct Answer is :   10x + 15y = 125
Q15Jimmy bought a few books and pens for $54. Cost of each book is $6 and cost of each pen is $2. Identify an equation that models the cost of the books and pens Jimmy bought, if x represents the number of books and y represents the number of pens.
A. 2x + 6y = 54
B. 2x - 5y = 54
C. 6x - 2y = 54
D. 6x + 2y = 54

Solutions
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Step: 1
Cost of a book = $6
Step: 2
Cost of a pen = $2
Step: 3
(Cost of a book × Number of books) + (Cost of a pen × Number of pens) = Total cost
  [Verbal model.]
Step: 4
6x + 2y = 54
  [Substitute the values.]
Step: 5
The equation that models the total cost of the books and pens Jimmy bought is 6x + 2y = 54.
Correct Answer is :   6x + 2y = 54

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