Who wants a treat!
Mr. Thomas & Family go for a Sunday feast. If they order 5 pizza, 4 burgers and 6 mocktails, the bill would be $110. But if the order is for 7 pizza, 2 burgers and 3 mocktails, the bill would go down by $20. Assume that the price of each type of item remains the same. Using given information, can we know the exact price of one
(a) pizza (b) burger (c) mocktail
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1 solution
Let us say that the price of a pizza, a burger and a mocktail are P, B and M respectively. Then
5 P + 4 B + 6 M = 1 1 0
7 P + 2 B + 3 M = 1 0 0
If we multiply the second equation by 2 (notice that coefficients of B and M would become equal by doing so), and then subtract it from the first, we get 1 4 P − 5 P = 2 0 0 − 1 1 0
P = 1 0
Hence, we get the exact price of a pizza. But the price of a burger and mocktail cannot be determined exactly. We only know they are related by the equation
2 B + 3 M = 3 0
(by substituting the value of P back in any equation)
The reason this happens is that we have three variables and only two equations. As the quantity (coefficients) of two unknown items was proportionate, we could eliminate them and find the exact value of the third.