Problem of the Week

__9/17/18__

**Spare Tire**

Your uncle buys a new car that comes with five new tires, one for each wheel and one spare tire. He decides to be economical by using the spare tire as much as the other four tires. If he drives 68,000 miles, what will be the wear in miles on each tire?

__9/10/18__

A certain product is sold as either a liquid or a powder. Consumers were interviewed, and a survey revealed that—

1/5 do not use the product,

1/3 do not use the powder form,

427 use both the liquid and powder form, and

2/7 do not use the liquid form.

How many consumers were in the survey?

**Solution**

735 consumers. Divide the consumers into four sets:

*A*: They do not use the products.
*B*: They do not use the powder form.
*C*: They use both liquid and powder.
*D*: They do not use the liquid form.

We know that
*A*+ *B*= 1/3 of the total,
*A*+ *D*= 2/7 of the total,
*A*= 1/5 is the total, and
C = 427.

Then, *B *is 1/3-1/5 = 2/15 of the total. *D*is 2/7-1/5 = 3/35 of the total. *A*+ *B*+ *D*is 44/105 of the total. *C*is the remaining 61/105 of the total. The number of consumers interviewed is 427/(61/105) = 735.

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