The price of one packet of cheese is $4.30. Computed using the system of equations.
A system of equations is a set of equations involving the same variables, used to solve the value for each variable satisfying all equations.
In the question, we are informed that Calvin bought 5 packets of cheese and 3 burgers for $29.99. At the same price, Alex bought 3 packets of cheese and 7 burgers for $32.71.
We are asked the price of one packet of cheese.
We assume the price of one packet of cheese to be $x, and that of one burger to be $y.
The cost equations of Calvin and Alex can be made as follows:-
For Calvin:
The number of packets of cheese bought = 5.
The total price paid for packets of cheese = $5x.
The number of burgers bought = 3.
The total price paid for burgers = $3y.
Thus his total cost equation is 5x + 3y = 29.99.
For Alex:
The number of packets of cheese bought = 3.
The total price paid for packets of cheese = $3x.
The number of burgers bought = 7.
The total price paid for burgers = $7y.
Thus his total cost equation is 3x + 7y = 32.71.
Thus, we have a system of equations:
5x + 3y = 29.99 ... (i),
3x + 7y = 32.71 ... (ii).
To solve the equations, we multiply (i) with 7, and (ii) with 3 to get:
35x + 21y = 209.93 ...(iii)
9x + 21y = 98.13 ... (iv).
Subtracting (iv) from (iii), we get:
26x = 111.8.
Dividing this whole equation by 26, we get:
x = 4.3.
Thus, the price of one packet of cheese is $4.30. Computed using the system of equations.
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