Lesson More complicated word problems to solve using a single linear equation

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More complicated word problems to solve using a single linear equation

Problem 1

The cost of petrol rises by 2 cents a liter. Last week a man bought 20 liters at the old price.
This week he bought 10 liters at the new price. Altogether, the petrol costs $9.20. What was the old price for 1 liter?

Solution

Let x be the old price of petrol per liter.


Then you have this "money" equation from the condition


20x + 10*(x+2) = 920   cents,   where x is old price in cents for 1 liter.


20x + 10x + 20 = 920,

30x = 920-20,

30x = 900  ====>  x =  = 30.


Answer.  The old price for one liter of petrol was   30 cents = $0.30 per liter.

Problem 2

Mary planted some flowers. Jenny planted four times as many flowers as Mary, and Rina planted 4 fewer flowers than Mary.
Together they have a total of 44 flowers. How many flowers did Mary plant?

Solution

Let x be the number of flowers planted by Mary.

Then the number of flowers planted by Jenny is 4x, according to the condition,

and  the number of flowers planted by Rina is  (x-4).


From the condition, you have this equation for the total number of flowers 

x + 4x + (x-4) = 44.


Simplify and solve it for x.

x + 4x + x - 4 = 44,

6x - 4 = 44,

6x = 44 + 4 = 48  ====>  x =  = 8.


Answer.  Mary planted  8  flowers;  Jenny  4*8 = 32 flowers  and  Rina planted  8 - 4 = 4 flowers.

Problem 3

Heather, Chang, and Justin served a total of 93 orders Monday at the school cafeteria.
Chang served 2 times as many orders as Justin. Heather served 5 more orders than Justin. How many orders did they each serve?

Solution

Justin + Heather + Chang = 93
           ||      ||
J      + (J+5)   + 2J    = 93

4J + 5 = 93  ====>  4J = 93 - 5 = 88   ====>  J =  = 22.


Answer.  Justin served 22 orders, Heather 22+5 = 27  and  Chang served 2*22 = 44.

Problem 4

Louann and Carla received equal scores on a test made up of multiple choice questions and an essay.
Louann got 14 multiple choice questions correct and received 24 points for her essay.
Carla got 16 multiple choice questions correct and received 14 points for her essay.
How many points was each multiple choice question worth?

Solution

Let x be the number of points per each multiple choice question.


In total, Louann received 14x + 24 points;

           Carla received 16x + 14 points.


These points are equal


    14x + 24 = 16x + 14,

or

    24 - 14 = 16x - 14x

       10   = 2x

        x   = 10/2 = 5.


ANSWER.  Each multiple choice question is worth 5 points.

Problem 5

A new cruise ship line has just launched 3 new ships: the Pacific paradise, the Caribbean paradise and the Mediterranean paradise.
The Caribbean paradise has 10 more deluxe staterooms that the Pacific paradise. The Mediterranean paradise has 32 fewer deluxe staterooms
than three times the number of deluxe staterooms on the Pacific paradise. Find the number of deluxe staterooms for each of
the ships if the total number of deluxe staterooms for the three ships is 623.

Solution

Let P be the number of staterooms on Pacific paradise.

Then the number of staterooms on Caribbean paradise is P+10,

and the number of staterooms on Mediterranean paradise is 3P-32.

The equation is

P + (P+10) + (3P-32) = 623.

Simplify and solve for P:

5P - 22 = 623  --->  5P = 623 + 22 = 645  --->  P =  = 129 staterooms.

Answer.  Pacific has 129 staterooms, Caribbean has 139 staterooms and  Mediterranean has 355 staterooms.

On solving single linear equations and relevant word problems see the lessons
    - HOW TO solve a linear equation
    - Simple word problems to solve using a single linear equation
    - Typical word problems to solve using a single linear equation
    - Typical problems on buying and selling items
    - Typical investment problems
    - Advanced word problems to solve using a single linear equation
    - HOW TO algebraize and solve these problems using one equation in one unknown
    - Challenging word problems to solve using a single linear equation
    - Selected word problems to solve by reducing to single linear equation
    - Solving some business-related problems
    - HOW TO solve these simple word problems MENTALLY without using equations
    - Using time equation to solve some Travel and Distance problems
    - Using price equation to solve some business related problems
    - Solving problems by the backward method
    - Solving more complicated problems by the backward method
    - Solving entertainment problems on shortage of money
    - OVERVIEW of lessons on solving linear equations and word problems in one unknown
in this site.

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