Multiple choice

In a food store, the average weight of apple boxes increases by 800 grams when a new type of apple boxes is added. If the average weight of the new apple boxes is 2 kilograms more than the average weight of the old apple boxes, what is the ratio of the number of old apple boxes to the number of new apple boxes?

  1. 3 : 2

  2. 2 : 3

  3. 1 : 3

  4. 3 : 1

  5. a
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let N1 be the number of old boxes with average weight A1, and N2 be the number of new boxes with average weight A2 = A1 + 2. The new average is (N1*A1 + N2*(A1+2)) / (N1+N2) = A1 + 0.8. N1*A1 + N2*A1 + 2*N2 = (A1 + 0.8)(N1 + N2) = N1*A1 + N1*0.8 + N2*A1 + N2*0.8. 2*N2 = 0.8*N1 + 0.8*N2. 1.2*N2 = 0.8*N1. N1/N2 = 1.2/0.8 = 3/2.

AI explanation

Let the number of old apple boxes be n, the number of new apple boxes be m, and the average weight of the old boxes be A. The new boxes have an average weight of A + 2 kilograms. The total increase in average weight is 0.8 kilograms across all the boxes. Using the method of deviations or balancing the overall average, the total extra weight brought by the new boxes equals the total increase for all boxes: m(A + 2 - A) = (n + m)(0.8). Solving 2m = 0.8n + 0.8m gives 1.2m = 0.8n, which simplifies to the ratio n : m = 3 : 2.

Keep practicing — related questions