The Science Museum charges ₹14 for adult admission and ₹11 for each child. For 68 people from the school educational trip, the total cost was ₹784.
Taking x as the number of adults and y as the number of children, answer the following questions:
(i) Form the pair of linear equations representing the given situation.
(ii) Fill in the blanks: The lines formed by the pair of linear equations are ...
(iii) Find the number of adults visiting the Museum.
OR
(iv) Find the number of children visiting the Museum.
CASE STUDY 3:
A coaching institute of Mathematics conducts classes in two batches, I and II, with poor and rich children. In batch I, there are 20 poor and 5 rich children. In batch II, there are 5 poor and 25 rich children. The total monthly collection from batch I is ₹9000 and from batch II is ₹26,000. Assume that each poor child pays ₹x and each rich child pays ₹y per month.
Answer (2)
Let's tackle the problem step-by-step:
(i) Form the pair of linear equations representing the given situation:
We know that the total number of people is 68. Thus, the equation representing this situation is: x + y = 68 where x is the number of adults and y is the number of children.
The total cost for the 68 people is ₹784. Since each adult's admission costs ₹14 and each child's admission costs ₹11, the equation for the cost is: 14 x + 11 y = 784
So, the pair of linear equations is:
x + y = 68 14 x + 11 y = 784
(ii) Fill in the blanks: The lines formed by the pair of linear equations are...
The lines formed by this pair of linear equations are intersecting , which means they meet at a single point representing the unique solution to the system.
(iii) Find the number of adults visiting the Museum:
We will solve the equations using the substitution or elimination method.
First, solve the first equation for y : y = 68 − x
Substitute y in the second equation: 14 x + 11 ( 68 − x ) = 784
Simplifying, we get: 14 x + 748 − 11 x = 784 3 x = 784 − 748 3 x = 36 x = 3 36 x = 12
So, there are 12 adults visiting the museum.
(iv) Find the number of children visiting the Museum:
Using x = 12 in y = 68 − x : y = 68 − 12 y = 56
So, there are 56 children visiting the museum.
The pair of linear equations representing the situation are x + y = 68 and 14 x + 11 y = 784 . There are 12 adults and 56 children visiting the museum. The lines of these equations intersect, indicating a unique solution.
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