SOLUTION: Walmart sells thermometers ($6) and hot-water bottles ($2). In December, Walmart’s total sales were $2,132. Customers bought 4 times as many thermometers as hot-water bottles. Ho

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Walmart sells thermometers ($6) and hot-water bottles ($2). In December, Walmart’s total sales were $2,132. Customers bought 4 times as many thermometers as hot-water bottles. Ho      Log On


   

Question 1151699: Walmart sells thermometers ($6) and hot-water bottles ($2). In December, Walmart’s total sales were $2,132. Customers bought 4 times as many thermometers as hot-water bottles. How many of each did Walmart sell?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Solving with formal algebra....

Let x = number of hot water bottles
Then 4x = number of thermometers

The cost of 4x thermometers at $6 each and x hot water bottles at $2 each was $2132.

4x%286%29%2Bx%282%29+=+2132
24x%2B2x+=+2132
26x+=+2132
x+=+2132%2F26+=+82

ANSWER:
The number of hot water bottles sold was x=82.
The number of thermometers sold was 4 = 328.

CHECK:
82(2)+328(6) = 164+1968 = 2132

(2) An informal solution method, which leads to virtually the same calculations....

Since the number of thermometers sold was 4 times the number of hot water bottles, imagine "packages" each containing 4 thermometers and one hot water bottle.
The cost of each of those packages is 4($6)+1($2) = $24+$2 = $26.
The number of those packages sold to make $2132 is 2132/26 = 82.
82 packages each containing 4 thermometers and 1 hot water bottle makes a total of 328 thermometers and 82 hot water bottles.

Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the number of the hot-water bottles.


Then the number of the thermometers is 4x, according to the condition.


To find x, you have this revenue equation


    6*(4x) + 2x = 2132    dollars.


Simplify and solve fot x


    24x + 2x = 2132

    26x      = 2132

      x      = 2132/26 = 82.


ANSWER.  82 bottles and 4*82 = 328 thermometers.

Solved.


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            There is another way to solve the problem mentally,  without using equations. 

According to the condition, you may group the items in subsets,

placing 1 bottle and 4 thermometers in each subset.


Then the cost of each subset is  2*1 + 4*6 = 2 + 24 = 26 dollars,

and the number of subsets is  2132/26 = 82.


It gives you the same answer.