Question #22350

From a survey of 100 students, a marketing research company found that 65 students owned; iPods; 55 owned cars, and 25 owned both cars and iPods.
(a) How many students owned either a car or an iPod ( but not both)
(b) How many students do not own either a car or an iPod?

Expert's answer

3a. In last week's football game, Ralph scored 6 lessthan twice what Tommy scored. The sum of their scores is 30. How many points

did Ralph and Tommy score individually?

Answer.Let R be the scores of Ralph, and T be the scores ofTommy.

Then

R = 2T-6

and

R+T = 30

Therefore 30 = R+T =2T-6+T = 3T-6

3T = 36

T=12

whence

R = 30-T = 18

Thus Ralph scores 18, and Tommy 12

--------------------

3b. The ages of three sisters are three even consecutiveintegers. If the sum of the 1st, four times the 2nd, and twice the 3rd is 86,

what are the three ages?

Answer.

Let X be the age of the youngest sister.

Then two other sisters have ages X+2 and X+4respectively.

We also know that

X + 4(X+2) + 2(X+4) = 86

X + 4X + 8 + 2X + 8 = 86

7X = 86 - 16 = 70

X = 10

So the ages of sisters are

10, 12, 14

--------------------

3c. You are buying a computer at a markdown price of$960. If the markdown price was 20% off the original price, how much was the

computer originally?

Answer.

Let X be the original price.

Then the markdown price constitute 80% of X, that is

960 = 0.8 X

whence

X = 960/0.8 = 1200

did Ralph and Tommy score individually?

Answer.Let R be the scores of Ralph, and T be the scores ofTommy.

Then

R = 2T-6

and

R+T = 30

Therefore 30 = R+T =2T-6+T = 3T-6

3T = 36

T=12

whence

R = 30-T = 18

Thus Ralph scores 18, and Tommy 12

--------------------

3b. The ages of three sisters are three even consecutiveintegers. If the sum of the 1st, four times the 2nd, and twice the 3rd is 86,

what are the three ages?

Answer.

Let X be the age of the youngest sister.

Then two other sisters have ages X+2 and X+4respectively.

We also know that

X + 4(X+2) + 2(X+4) = 86

X + 4X + 8 + 2X + 8 = 86

7X = 86 - 16 = 70

X = 10

So the ages of sisters are

10, 12, 14

--------------------

3c. You are buying a computer at a markdown price of$960. If the markdown price was 20% off the original price, how much was the

computer originally?

Answer.

Let X be the original price.

Then the markdown price constitute 80% of X, that is

960 = 0.8 X

whence

X = 960/0.8 = 1200

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