EQUATIONS AND RELATIONSHIPS WORKSHEET

Problem 1 :

3 less than four times a number is equal to 2 more than three times the same number. Write an equation which models this situation.

Problem 2 :

The average of 3 consecutive odd numbers is equal to 9. Write an equation which models this situation and also find the largest of the three consecutive numbers.

Problem 3 :

The cost of each pen in a store is $0.75. Tim would like to buy some pens. Write an equation to determine how much money that Tim has to pay. And also find the cost of 4 pens. 

Problem 4 :

Sonia used $12.50 to buy a new journal. Write an equation to determine how much money that Sonia has left in her saving account. After the journal was bought, if she had $34.25 left, how much money did she have initially ?

Problem 5 :

Tim is paid $8 more than the number of bags of peanuts he sells at the baseball stadium. The table shows the relationship between the money Tim earns and the number of bags of peanuts Tim sells. Identify the independent and dependent variables, and write an equation that represents the relationship.

Problem 6 :

The Falcons won their football game with a score of 30 to 19. Kevin scored 12 points for the Falcons. Write an equation to determine how many points Kevin’s teammates scored.

Problem 7 :

A taxi charges a flat rate of $3, plus an additional $1.50 per mile. How can we model this situation as an equation ? And also find the fare for 10 miles of distance.

Problem 8 :

A cab service charges a flat rate of $10 for the first 5 miles and $2 for each additional miles. Write the equation which gives the total cost for more than 5 miles and calculate the total cost for travelling 12 miles.

Answers

1. Answer :

Let x be the number.

4x - 3 = 3x + 2

2. Answer :

Three consecutive odd numbers can be assumed as given below.

x, (x + 2), (x + 4)

Given : Average of three consecutuve odd numbers is 9.

Solve for x.

x + (x + 2) + (x + 4) = 27

x + x + 2 + x + 4 = 27

3x + 6 = 27

3x = 21

x = 7

The largest of the three consecutuve number is

= x + 4

= 7 + 4

= 11

3. Answer :

To solve this problem, we have to assign variables for the unknown quantities "number of pens" and "Total money paid"

Let x be the number of pens and y be the total money paid for x number of pens. 

Now, we have to find the relationship between the two quantities x and y and form it as an equation. 

Since, each pen costs $0.75, the cost of x number of pens is $0.75x.

Since y stands for the total money paid for x number of pens, we have

y = $0.75x

If Tim buys 4 pens, we have to substitute x = 4 in the above equation to know the total money paid for 4 pens.

 y = $0.75(4)

y = $3

Therefore, the cost of 4 pens is $3.

4. Answer :

Let x be the money that Sonia had initially (Before she bought the journal)

Let y be the money that she has left in her account (After she  bought the journal).

She used $12.50 to buy journal from x dollars. Then the money that she has left in her savings account is 

x - $12.50

Since y stands for the money that she has left in her account after she bought the journal, we have 

y = x - 12.50

If she had $34.25 left, we have to plug y = 34.25 in the above equation to know the money that she had initially.

34.25 = x - 12.50

46.75 = x

So, if she had $34.25 left, she would have had $46.75 initially.

5. Answer :

The number of bags is the independent variable, and the money Tim earns is the dependent variable.

Since x stands for number of bags and it is given that he earns $8 more than number of bags (x), the money earned by Tim is

x + 8

Since y stands for money earned by Tim, we have

y = x + 8

So, the equation y = x + 8 expresses the relationship between the number of bags Tim sells and the amount he earns.

6. Answer :

Let x be the points scored by Kevin's team mates. 

The points scored by Kevin is 12. 

Kevin and team mates together won the game. So, the winning point is the sum of the points scored by Kevin and his team mates. 

That is, 

12 + x

Since the winning score is 30 points, we have 

12 + x = 30

So, 12 + x = 30 is the equation to determine how many points Kevin’s teammates scored.

7. Answer :

Let x be the number of miles and y be the total fare for x number of miles. 

Since taxi, charges $1.50 per mile, fare for x number of miles is

$1.50x

Taxi charges a flat rate of $3. Then the total fare is 

$1.50x + $3

Since y stands for total fare for x number of miles, we have

y = $1.50x + $3

To find the fare for 15 miles, substitute x = 15.

y = $1.50(10) + $3

y = $15 + $3

y = $18

So, the fare for 10 miles of distance is $18.

8. Answer :

Let x be the number of miles where x > 5 and y be the total cost.

$10 is charged for the first 5 miles and $2.50 per mile is charged for each additional mile, that is for (x - 5) miles.

Therefore,

y = $10 + $2.5(x - 5)

y = $10 + $2.5x - $12.5

y = $2.5x - $2.5

To find the fare for 12 miles, substitute x = 12.

y = $2.5(12) - $2.5

y = $30 - $2.5

y = $27.5

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.