So a baker sells plain cakes for $7 and decorated cakes for $11. On a busy Saturday, the baker started with 120 cakes and sold and sold all but 3. His takings for the day were $992. How many plain cakes did he sell that day, and how many decorated cakes did he sell that day?
Responses (1)
7x + 11y = 992 plain cakes for $7 and decorated cakes for $11
x + y = 117 120 cakes and sold and sold all but 3
You have two lines. They look like this: www.wolframalpha.com/input/?i=plot+x+%2B+y+%3D+117,+7x+%2B+11y+%3D+992
Where they cross, the values of x and y satisfy both equations simultaneously, so it is called a simultaneous system. There are two ways to find that point. Substitution is when you solve one equation for one variable and substitute that into the other equation.
y = 117 - x Substitute this for y in the other equation.
7x + 11(117 - x) = 992
7x + 1287 - 11x = 992
-4x = -295
x = 73.75, y = 43.25
Elimination is when you add the equations in a way to eliminate one variable. Otherwise the process is the same.