The number of chicken dish is 131 dishes while the number of lobster dishes is 119 dishes
<h3>How to find the number of each type of dish.</h3>
Let
- x = number of chicken dish and
- y = number of lobster dish
<h3>How to determine the equations for the linear system</h3>
Since it cost $40 per dish for chicken dish, the total cost of chicken dish is 40x.
Also, since it cost $70 per dish for lobster dish, the total cost of lobster dish is 70y
So, the total cost of dish is T = 40x + 70y
Also, we know that the total cost of dish is $13,570.
So, 40x + 70y = 13570 (1)
Also, there are going to be 250 guest at the dinner and thus 250 dishes.
So, the total number of dishes is x + y = 250
So, x + y = 250 (2)
So, the equations of the linear system are
40x + 70y = 13570 (1)
x + y = 250 (2)
<h3>How to determine the solution for the linear system</h3>
Since
40x + 70y = 13570 (1)
x + y = 250 (2)
From (2), x = 250 - y
Substituting x into (1), we have
40x + 70y = 13570 (1)
40(250 - y) + 70y = 13570 (1)
10000 - 40y + 70y = 13570
30y = 13570 - 10000
30y = 3570
y = 3570/30
y = 119
Substituting y = 119 into x, we have
x = 250 - y
x = 250 - 119
x = 131
Therefore, the number of chicken dish is 131 dishes while the number of lobster dishes is 119 dishes
Learn more about equation of linear system here:
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d^2/4 = 132.7