A watch costs $48 more than a clock.The cost of the clock is 4/7 the cost of the watch.Find the total cost of the two items.

Question

How can this question be expressed & explained in equation?

Answer 1

The key to word (story) problems is to correctly translate the words and phrases into concise, precise math expressions -- variables and operations.

 

The problem asks us to find the cost of the two items, so

           let C= cost of clock and

               W = cost of watch

 

"A watch costs $48 more than a clock"      means     W = 48 + C

"cost of the clock is 4/7 the cost of the watch"      means      C = (4/7)W

"Find the total cost of the two items"       means     report W+C       (notice this!)

 

Now, the math is easy:

            4W      = 192    + 4C      (first equation multiplied by 4)

            4W    =           7C         (second equation multiplied by 7)

        -------------------------

              0     =   192  - 3C       (subtract equations -- this is elimination method)

               C =  64                    (put C on left and divide both sides by 3)

What is W?

              W = 48 + C         (first equation)

              W =  112

Now, what is the total cost of the two items?

              $64 + $48 = $112

 

Checking (very important):

    Is 112 = 48 + 64    ?    yes!

 

    Is  64 = (4/7)*112   ?

         64 =  64       yes!