Lesson Typical problems on buying and selling items

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Typical problems on buying and selling items


Problem 1

White chocolate cost  $20.00  per bar,  and dark chocolate cost  $25.00  per bar.
If Anne bought  15  bars of chocolate for  $340.00,  how many bars of dark chocolate did she buy?

Solution 

Let x be the number of dark chocolate bars Anne bought.

Then the number of the white chocolate bars is 15-x.


Write the total money equation

    25x + 20*(15-x) = 340  dollars.


Simplify and find x

    25x + 300 - 20x = 340

    25x - 20x = 340 - 300

        5x    =     40

         x    =     40/5 = 8


ANSWER.  Anne bought 8 dark chocolate bars.


CHECK.  25*8 + 20*(15-8) = 200 + 140= 340 dollars, total.  ! Correct !

Problem 2

At the city museum,  child admission is  6.30  and adult admission is  $9.60.
On  Monday,  158  tickets were sold for a total sales of  $1193.40.
How many child tickets were sold that day?

Solution 

Let x be the number of child tickets sold that day.

Then the number of adult tickets sold is (158-x).


Write the total money equation

    6.30*x + 9.60*(158-x) = 1193.40  dollars.


Simplify step by step and find x

    6.30x + 9.60*158 - 9.60x = 1193.40

    6.30x - 9.60x = 1193.40 - 9.60*158

        -3.30x    =   -323.40

             x    =   %28-323.40%29%2F%28-3.30%29 = 98.


ANSWER.  98 child tickets.


CHECK.  6.30*98 + 9.60*(158-98) = 1193.40  dollars, the total revenue.  ! correct !

Problem 3

30  books and magazines were on a shelf.  Each book costs  $5  while each magazine costs  $3.
The total cost of the books was  $6  more than the magazines.
How many books were on the shelf.

Solution 

x books, 30-x magazines.

Money equation is

    5x -3*(30-x) = 6  dollars.


Simplify and find x

    5x - 90 + 3x = 6

    8x = 90+6 = 96

     x        = 96/8 = 12.


ANSWER.  12 books.

Problem 4

A machine requires  6  hours to make a unit of Product  A  and  5  hours to make a unit of  Product  B.
Last month the machine operated for  481  hours,  producing a total of  89  units.
How many units of  Product  A  were produced?

Solution 

Let x be the number of units of A-product.
Then the number of units of B-product is 89-x.


Write the full elapsed time equation

    6x + 5*(89-x) = 481.


Simplify and find x

    6x + 445 - 5x = 481

    6x - 5x = 481 - 445

       x    = 36.


ANSWER.  36 units of A-product were produced.


My other lessons on solving single linear equations and word problems in one unknown are
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