A chemist wishes to prepare 20 litres of a 25% saline solution by mixing a 10% saline…
MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables
Problem
A chemist wishes to prepare 20 litres of a 25% saline solution by mixing a 10% saline solution with a 50% saline solution.
(i) Let x litres of the 10% solution and y litres of the 50% solution be required. Write two linear equations expressing the total volume and the total amount of salt in the final mixture.
(ii) List any two convenient ordered pairs for each equation and tabulate them.
(iii) Plot the two equations on the same set of axes, taking the 10% solution on the x-axis and the 50% solution on the y-axis, and draw both straight lines.
(iv) From the point where the two lines intersect, find the precise volumes of the 10% and 50% solutions needed.
(v) Suppose the chemist has only 6 litres of the 50% solution available. Use the graph to decide whether it is still possible to prepare 20 litres of the 25% solution. Give a brief justification based on the position of the required point relative to the drawn lines.