To solve the problem, we can set up a system of linear equations based on the information given. Let's define the variables as follows:
Let B represent the cost of one burger.
Let S represent the cost of one shake.
Let F represent the cost of one order of fries.
We are given two scenarios:
1. 3 burgers, 7 shakes, and 1 order of fries cost Rs. 120.
2. 4 burgers, 10 shakes, and 1 order of fries cost Rs. 164.50.
We can now create two equations based on the given scenarios:
(1) 3B + 7S + F = 120 (Equation 1)
(2) 4B + 10S + F = 164.50 (Equation 2)
To solve for the cost of one burger (B), one shake (S), and one order of fries (F), we need to solve this system of linear equations. We can use the elimination method or the substitution method to find the values for B, S, and F.
First, notice that in both (1) and (2), there is one F. We can use this to eliminate F by subtracting equation (1) from equation (2).
So we subtract each term of equation (1) from equation (2):
(4B + 10S + F) - (3B + 7S + F) = 164.50 - 120
This simplifies to:
4B - 3B + 10S - 7S + F - F = 164.50 - 120
B + 3S = 44.50 (Equation 3)
At this point, we have two equations, (1) and (3), with two unknowns (B and S):
(1) 3B + 7S + F = 120
(3) B + 3S = 44.50
We cannot directly solve for any variable, as we need one more piece of information which is not provided explicitly in the problem. This missing piece of information is the cost of the fries (F) in either (1) or (3) taken in isolation. We can, however, use these equations to express F in terms of B and S, and then find the individual prices.
Let's express F from equation (1):
F = 120 - 3B - 7S
Now we substitute the value of F into equation (3):
B + 3S = 44.50
B = 44.50 - 3S
Substitute B in the equation for F:
F = 120 - 3(44.50 - 3S) - 7S
F = 120 - 133.50 + 9S - 7S
F = -13.50 + 2S
Now we have F expressed in terms of S, but since we don't have the cost of a single item explicitly, we cannot calculate the exact values for B, S, and F without an additional piece of information or equation.
Typically, the problem would give us the cost of either B, S, or F separately, allowing us to solve for the other variables. Without this additional piece of information, we can't find the exact numerical values for the prices of a burger, a shake, or fries.
Since the problem does not give us all the information we need to find a numerical solution, it might be incomplete or there might be a missing piece of data. Please check if there is any additional information that was provided with the problem.