Final answer:
By setting up a system of linear equations and solving it using the elimination method, we find that the student bought 18 books for sh 40 each and 12 books for sh 30 each.
Step-by-step explanation:
The question involves solving a system of linear equations to find out how many books of each kind were bought. We have two types of books with different costs and a total cost, and we want to determine the number of each type purchased within the total.
Let's define two variables: Let x be the number of books costing sh 40, and let y be the number of books costing sh 30. We have two equations based on the given information:
- The total number of books is 30: x + y = 30
- The total amount spent is sh 1080: 40x + 30y = 1080
To solve this system, we can use the substitution or elimination method. Here, the elimination method may be more straightforward.
Multiply the first equation by 30 to match the coefficient of y in the second equation:
30x + 30y = 900
Now subtract this equation from the second equation to eliminate y:
(40x + 30y) - (30x + 30y) = 1080 - 900
10x = 180
Divide both sides by 10 to find the value of x:
x = 18
Now substitute x back into the first equation to find y:
18 + y = 30
y = 30 - 18
y = 12
Therefore, the student bought 18 books costing sh 40 each and 12 books costing sh 30 each, which corresponds to option b).