Multiple choice

Number of Vehicles Number of Families 0 3 1 2x 2 5 3 6 4 6 The above table shows the number of vehicles, families have. If the average number of vehicles is 2, how many families are there?

  1. 48

  2. 46

  3. 32

  4. 28
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average = (Sum of (vehicles * families)) / Total families. Sum = 0*3 + 1*2x + 2*5 + 3*6 + 4*6 = 0 + 2x + 10 + 18 + 24 = 2x + 52. Total families = 3 + 2x + 5 + 6 + 6 = 2x + 20. Average = (2x + 52) / (2x + 20) = 2. 2x + 52 = 4x + 40. 2x = 12, x = 6. Total families = 2(6) + 20 = 32.

AI explanation

The total number of families is the sum of the frequencies, which equals 3 plus 2x plus 5 plus 6 plus 6, simplifying to 20 plus 2x. The total number of vehicles is calculated by multiplying each vehicle count by its number of families, giving (0 times 3) plus (1 times 2x) plus (2 times 5) plus (3 times 6) plus (4 times 6), which simplifies to 2x plus 52. Since the average number of vehicles is 2, we set up the equation (2x plus 52) divided by (20 plus 2x) equals 2. Solving for x gives 2x plus 52 equals 4x plus 40, so x is 6. Substituting x equals 6 into the expression for total families yields 20 plus 2 times 6, which equals 32.

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