A grocery store sells boxes of two kinds of cereals, wheat-based and r

Official Explanation:

Method One: Algebraic Approach

This approach is longer, more time-consuming, but easier to understand.

We can set up a weighted average. Let W be the number of boxes of wheat-based cereals, and R be the number of boxes of rice-based cereals. Here’s the weighted average formula:

\(\frac{(60R+48W)}{(R+W)​​}\)= 50

Multiply both sides by (R + W)

60R + 48W = 50R + 50W

10R + 48W = 50W

10R = 2W

5R = W

\(\frac{R}{W}\) = \(\frac{1}{5}\)

Answer = (C)

Method Two: Intuitive Geometric Approach

This approach is lightning fast but harder to understand.

Look at the the two distance of the individual averages from the weighted average. Wheat-based cereals are at 60, 10 units away from 50. Rice-based cereals are at 48, just 2 units from 50. The ratio of the distances is 10 to 2, or 5:1, so the ratio of the group sizes must be the reciprocal, 1:5.

Answer = (C)

Can you solve it as follows? If we're trying to determine the ratio of Rice:Wheat

R:W
60/50R=48/50W
Cross multiply
60*50R=48*50W
3000R=2400W
R/W=2400/3000
1-4/5= 1/5

We can solve this question using mixtures method
wheat rice
48 60

50

10 2

(60-50=10, 50-48=2)
=>wheat:rice ratio = 10:2 = 5:1
=>rice:wheat ratio = 1/5 => option c