Lesson Spending money according to dates

This Lesson (Spending money according to dates) was created by by ikleyn(52776)

: View Source, Show
About ikleyn:

Spending money according to dates

Problem 1

Mr. X had a habit of spending money according to dates. For example, if date was 19 he was spending $19, and if date was 15 he was spending $15.
One night he calculated total spending of 5 consecutive days - Monday to Friday, and he found that he spent $61 in 5 days.
So, identify the dates. (Assume that everyday spending is integer number of dollars).

Answer. There is only one solution:
27 and 28 of February and 1, 2, and 3 of March.
(27 + 28 + 1 + 2 + 3 = 61).

Solution

If these days would be inside one month, then the dates are (x-2), (x-1), x, (x+1) and (x+2), where x is the date in the middle of 5 days.
Then the sum must be multiple of 5, since

(x-2) + (x-1) + x + (x+1) + (x+2) = 5x.

But the integer 61 is not multiple of 5. Contradiction.

Hence, the dates are partly the end of some month and the beginning of the next month.

Then, it is easy to check that the dates 27, 28, 1, 2 and 3 satisfy the condition 27 + 28 + 1 + 2 + 3 = 61.
Next, it is easy to see that there is no other solution.

Problem 2

Same problem if Mr. X spent $63 in 5 consecutive days. Identify the dates. Solve the problem yourself.

Problem 3

Next time Mr. X's spending was $90 of 6 consecutive days - Monday to Saturday.
Identify the dates. Solve the problem yourself.

My other lessons on Miscellaneous word problems in this site are

    - Some logic problems
    - How to algebreze and to solve word problems on numbers?
    - Problem on two-wheel and three-wheel bicycles
    - Problem on animals at a farm
    - Problem on pills in containers
    - What type of problems are these?
    - Virtual exchange between two persons
    - Word problems on reversing digits of numbers
    - Counting elements in sub-sets of a given finite set
    - How many subsets are there in a given finite set of n elements?
    - In how many ways the number 27720 can be split into a product of two co-prime factors?
    - Advanced problems on counting elements in sub-sets of a given finite set
    - Challenging problems on counting elements in subsets of a given finite set
    - Had they sold . . .
    - HOW TO algebreze and solve these problems?

    - How many coconuts are there in each of five baskets?
    - Tom the cat is brushing up his Math skills
    - How many lollipops do the children have?
    - Three grasshoppers play leapfrog along a line
    - The gardener's problem on a miracle tree in an enchanted garden
    - Water level rise in a tank after submerging bodies
    - Burning candles
    - Gaining clock problem
    - Finding the value of infinite continued fraction
    - Three circles touching externally
    - Solving minimax problems by the Linear Programming method
    - One unusual mimimax problem on joint work
    - Classic entertainment problems
    - More complicated but still elementary logic problems
    - Miscellaneous word problems for the day of April, 1
    - OVERVIEW of lessons on Miscellaneous word problems.

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

This lesson has been accessed 2350 times.