WRITING EQUATIONS TO MODEL RELATIONSHIPS

Solved Problems

Problem 1 :

5 more than three times of a number is equal to 5 less than four times of the same number. Write an equation to model the above relationship. 

Solution :

Let x be the number.

3x + 5 = 4x - 5

Problem 2 :

The product of 7 and a number is equal to 10 less than 9 times of the same number. Write an equation to model the above relationship.  

Solution :

Let x be the number.

7x = 9x - 10

Problem 3 :

Suppose you receive $100 for a graduation present, and you deposit it in a savings account. Then each week thereafter, you add $5 to the account but no interest is earned. Write an equation which results the money that you have in your account after some weeks.

Solution :

Let x be the number of weeks and y be the money in the account.

y = 100 + 5x

Problem 4 :

Kevin is spending money at an average rate of $5 per day. After 15 days he has $125 left. The amount left depends on the number of days that have passed. Write an equation which results the money that Kevin has left after some days.

Solution :

Let x be the number of days and y be the money he has left after x days.

Kevin spent $5 per day.

Amount of money spent by Kevin in 15 days :

= 15 ⋅ 5

= $75

Given : After 15 days, he has $125 left.

Aamount of money Kevin had intially :

= $75 + $125

= $200

Therefore, the equation which models the given sitution is

y = 200 - 5x

Problem 5 :

An electricain charges a flat rate of $25 and $8 for each hour he works. Write an equation which gives the total cost for hiring the electrician.

Solution :

Let x be the number of hours and y be the total cost.

y = 25 + 8x

Problem 6 :

A carpenter charges a flat rate of $36 for the first 4 hours and $7 for each additional hours.  Write an equation which gives the total cost for hiring the carpenter for a work lasting more than 5 hours.

Solution :

Let x be the number of hours and y be the total cost.

The carpenter charges a flat rate of $36 for the first 4 hours and $7 for each additional hour, that is for (x - 4) hours.

Therefore,

y = 36 + 7(x - 4)

y = 36 + 7x - 28

y = 7x + 8

In the equation above, x ≥ 4.

Problem 7 :

The cost of an apple is $2.50 and that of a banana is $0.80. Lily bought both the fruits for a total of 16 items and she paid $23. Write a system of equation which can be used to find the number of apples and number of bananas.

Solution :

Let x be the number of apples and y be the number of bananas.

Given : Total number of items bought is 16.

x + y = 16

Given : Lily paid $23 for her purchase.

2.5x + 0.8y = 23

Therefore, the required system is

x + y = 16

2.5x + 0.8y = 23

Problem 8 :

Peter won 27 games in a tournament. In each game Kevin won, he scored either 3 points or 4 points and he scored 93 points in all. Write a system of equation which can be used to find the number of 3-point games and 4-point games won by Kevin.

Solution :

Let x be the number of 3-point games and y be the number of 4-point games won by Kevin.

Given : Peter won 27 games.

x + y = 27

Given : Kevin scored eithet 3 points or 4 points in each game and he won 93 points in all.

3x + 4y = 93

Therefore, the required system of equation :

x + y = 27

3x + 4y = 93

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.