value of coins

Question

A collection of coins contains only 10-cent and 5-cent coins.There are x 5cent coins in the collection. Write an algebraic expression for of following.
* The total value of the coins if for every three 10-cent coins there are five 5-cent coins.

Answer 1

Let's make a list of the values according to their sequence.  This will allow us to see a pattern.

 

10 , 20 , 25 , 30 , 35 , 40 , 45  ----->   1st three

 

55 , 65 , 70 , 75 , 80 , 85 , 90   ----->   2nd three

 

100 , 110 , 115 , 120 , 125 , 130 , 135    ---->  3rd three

 

 

By now, you should see a pattern.  Look at the last number for each set.  45, 90, and 135.  If we keep going, the last number in each set would be a multiple of 45.  This means that in the 4th set, the total value of the coins would be 180.  Lets check that theory.

 

145 , 155 , 160 , 165 , 170 , 175 , 180

 

 

The last number here is indeed 180 .  So now we use this pattern to write the expression.

 

Let x = # of 5 cents coins

Let y = total value in cents

 

y = 45x

 

 

Answer 2

"for every three 10-cent coins there are five 5-cent coins"   is the same as

     "for every five 5-cent coins there are three 10-cent coins"

 

The value in cents is (number of coins)*(value of each coin).

 

                   5*5                   +              3*10              = 55 cents in a set  (here, x=5)

 

Now, there are five 5-cent coins in a set, so the number of sets is x/5 [truncated] and the value is:

      (x/5)*55 cents

        11x cents

 

Good time for an example:

    "for every three 10-cent coins there are five 5-cent coins" and there are ten 5-cent coins [note: x=10].

                    six 10-cent coins        and                                       ten 5-cent coins

                         60 cents                                             +               50 cents

                          $1.10    [yes, this is 11x cents]

 

  another example:

      nine 10-cent coins and fifteen 5-cent coins     [again three for each five]

              90 cents        +             75 cents

                  165 cents

                  $1.65       [yes, this is 11*15 cents]