Question

A farmer spends pounds 752 in buying horses and cows; if each horse costs pounds 37 and each cow pounds 23, how many of each does he buy.
(A). Horses=11, Cows=15
(B). Horses=12, Cows=12
(C). Horses=10, Cows=9
(D). Horses=7, Cows=19

Answer 1

Hint: Start by letting the number of horses be x and the number of cows be y. Using the condition given in the question form the equation. Now check for which option the equation of the line is satisfied.

Complete step-by-step solution -
Before starting with the solution, let us discuss the significance of linear equations in two variables. Linear equations in two variables represent the equation of a line on the Cartesian plane.
Now we will move to the solution to the given question. First, let us begin by letting the number of cows to be x and the number of horses to be y. As x and y are the numbers of horses and cows, respectively, they must be whole numbers.
Now according to the question, the cost of one horse is pounds 37, and the cost of one cow is pounds 23. It is also given that the total amount that the farmer spent was pounds 752. So, if we represent this data mathematically, we get
$37x+23y=752$
Now to find the answer to the above question we will check the options one by one.
First, let us start with option (a). For option (a), x=11 and y=15. If we put these values in the left-hand side of our equation, we get
$37\times 11+23\times 15$
$=752$
So, the equation is satisfied; hence the answer to the above question is option (a).

Note: Be careful with the signs and calculations as in such questions, the possibility of making a mistake is either of the sign or a calculation error. Also, we should be clear that a solution can represent different geometries when represented in planes with different dimensions, and all the points lying on these geometries would represent a solution to the linear equation. For example: when the solution of the above equation is represented on a number line, i.e., a single dimensioned plane, the geometry formed is just a point while on the Cartesian plane, it is represented by a straight line. Further, if we extend it to a 3-D plane, we will find the same solution will represent a plane.