In what ratio must a grocer mix two varieties of rice costing 128 and 143 per kg, respectively,to get a mixture of rice worth 137.75 per kg

To determine the ratio in which the grocer must mix the two varieties of rice costing $ 128 $ per kg and $ 143 $ per kg to get a mixture worth $ 137.75 $ per kg, we can use the concept of alligation.

Alligation is a method that enables us to find the ratio in which two or more ingredients at different prices must be mixed to produce a mixture of a desired price.

Let's denote the price of the first variety of rice as $ P_1 = 128 $ per kg, the price of the second variety as $ P_2 = 143 $ per kg, and the mean price of the mixture as $ P_m = 137.75 $ per kg.

The alligation formula is given by:

\[
\text{Ratio} = \frac{P_2 - P_m}{P_m - P_1}
\]

Substituting the given values:

\[
\text{Ratio} = \frac{143 - 137.75}{137.75 - 128}
\]

Let's calculate the values step by step:

\[
143 - 137.75 = 5.25
\]

\[
137.75 - 128

Discover how to calculate the ratio in which a grocer must mix two varieties of rice costing $128 and $143 per kg to obtain a mixture worth $137.75 per kg. This problem uses the concept of alligation, a method for finding proportions in mixtures of different prices.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation