Question

A farmer spends 752 pounds in buying horses and cows. If each horse costs 37 pounds and each cow 23 pounds, how many of each does he buy?
(a) 11 horses and 15 cows
(b) 7 horses and 20 cows
(c) 16 horses and 4 cows
(d) 13 horses and 17 cows

Answer 1

Hint: To solve this question, we will make a linear equation in two variables and then check the option by putting the values in them into the linear equation.

Complete step-by-step answer:
This question is an example of a linear equation in two variables. Linear equation in two variables in a type of linear equation which contains two independent variables x and y. Now, to solve the question, we have to make use of the data given in the question to make linear equations. It is given that each horse cost 37 pounds.
Let us assume that the farmer purchases x horses. We are given that the cost of one horse is 37 pounds. So, the cost of x horses will be = 37x.
Now, let us assume that the farmer purchased y number of cows. We are given that the cost of one cow is 23 pounds. So, the cost of y cows will be = 23y
Now, it is given that the total money spent by the farmer is = 752 pounds
In 752 pounds, the farmer buys x number of horses and y number of cows. So, our linear equation becomes:
37x + 23y = 752……………..(i)
We only have a single linear equation because the data given in the question is limited. So, we will find the solution of this equation by checking the options one by one:
Option (a): 11 horses and 15 cows. In this case the value of x = 11 and y = 15. We will now put these values in equation (i) :
37(11) + 23(15) = 752
407 + 345 = 752
752 = 752
So, this option satisfies the equation.
Option (b): 7 horses and 20 cows. In this case the value of x = 7 and y = 20. We will now put these values in equation (i):
37(7) + 23(20) = 752
259 + 460 = 752
719 = 752
Hence, this option does not satisfy the equation.
Option (c): 16 horses and 4 cows. In this case the value of x = 16 and y = 4. We will now put these values in equation (i):
37(16) + 23(4) = 752
592 + 92 = 752
684 = 752
Hence, this option does not satisfy the equation.
Option (d): 13 horses and 17 cows. In this case the value of x = 13 and y = 17. We will now put these values in equation (i):
37(13) + 23(17) = 752
481 + 391 = 752
872 = 752
Hence, this option does not satisfy the equation.
Hence, option (a) is correct.

Note: Instead of checking options one by one, we could have also done it graphically. In the graphical method, we check which of the points in the options are present on the line 37x + 23y = 752.