Lesson OVERVIEW of my additional lessons on solving single linear equations and word problems in one unknown

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OVERVIEW of my additional lessons on solving single linear equations and word problems in one unknown

My additional lessons on solving linear equations and word problems in one unknown in this site (section 2) are
    - One more lesson on solving problems by the backward method
    - Choose an unknown variable in a rational way for your problem
    - Entertainment problems on finding three unknowns using only one equation
    - Upper level word problems to solve using a single linear equation

List of lessons with short annotations

One more lesson on solving problems by the backward method

        Problem 1. Andy, Berlin and Cheryl had a total of 6750 stamps.
                               (1)   At first, Andy gave 50% of his stamps to Berlin.
                               (2)   Berlin then gave 1/3 of her stamps to Cheryl.
                               (3)   Finally, Cheryl gave 1/6 of her stamps to Andy.
                           In the end, the ratio of the number of Andy’s stamps to the number of Berlin’s stamps became 4:5.
                           Cheryl had twice the total number of stamps that Andy and Berlin had.
                           How many stamps did Berlin and Cheryl have in total at first?

Choose an unknown variable in a rational way for your problem

        Problem 1. Tom had 4/5 as many stamps as Michael. After Michael gave away 3/7 of his stamps,
                           Tom had 40 more stamps than Michael. How many stamps did Tom have?

        Problem 2. Mrs Johnson and her 2 sons Bernard and Raymond shared a sum of money.
                           The ratio received by Mrs Johnson to that received by Bernard was 5 to 2 .
                           The ratio of money received by Bernard to that received by Raymond was 3 to 4.
                           After Mrs Johnson gave 20% of her share to Raymond and B ernard donated 1/3 of his share to charity,
                           Raymond then had $4270 more than Bernard.
                           What was the sum of money shared by the three of them.

Entertainment problems on finding three unknowns using only one equation

        Problem 1. A school cafeteria cashier has collected $243 in one-dollar, five-dollar,
                           and ten-dollar bills. The number of one-dollar bills is eight more than 20 times the number of ten-dollar bills.
                           The cashier also has seven more than twice the number of ten-dollar bills in five-dollar bills. How many bills of each value does the cashier have?

        Problem 2. You are at the store, and are trying to remember how much bread, meat, and cheese you were supposed to buy.
                           The bread costs $3 per loaf, the meat costs $5 per pound, and the cheese costs $2 per pound.
                           You know that you are to buy fifteen items, that the total cost will be $51,
                           and that you are supposed to purchase one more meat than cheese. How many meat do you need to purchase?

Upper level word problems to solve using a single linear equation

        Problem 1. Three shops sold the same number of lanterns during the lantern festival.
                           Shop A sold 1/2 or its lanterns, Shop B sold 2/3 of its lanterns and
                           Shop C sold 3/4 of its lanterns. If the three shops had a total of 330 lanterns left,
                           how many lanterns did each shop sell?

        Problem 2. Jamie spent 3/4 of her money on 3 books of the same price.
                           Grace spent 5/9 of her money on 2 diaries.
                           They were each left with an equal amount of money.
                           One book costs $3.30 more than one diary.
                           How much money did they have altogether?

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