The following system of equations represents the given statement;
x = y+z
y = 2z
10x+15y+40z = 600
They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.
Step-by-step explanation:
Let,
Small pizza = x
Medium Pizza = y
Large Pizza = z
Cost of one small pizza = $10
Cost of one medium pizza = $15
Cost of one large pizza = $40
According to given statement;
They usually sells as many small pizzas as medium and large pizzas combined.
x = y+z
The number of medium pizzas sold is usually twice as many as large ones.
y = 2z
How many of each pizza must they sell to get $600.
10x+15y+40z = 600
The following system of equations represents the given statement;
x = y+z Eqn 1
y = 2z Eqn 2
10x+15y+40z = 600 Eqn 3
Putting value of x and y from Eqn 1 and 2 in Eqn 3;
[tex]10(y+z)+15(2z)+40z=600\\[/tex]
We know that y=2z from Eqn 2,
[tex]10(2z+z)+30z+40z=600\\20z+10z+70z=600\\100z=600[/tex]
Dividing both sides by 100;
[tex]\frac{100z}{100}=\frac{600}{100}\\z=6[/tex]
Putting z=6 in Eqn 2;
[tex]y=2(6)\\y=12[/tex]
Putting value of y and z in Eqn 1;
[tex]x=12+6\\x=18[/tex]
They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.
Keywords: linear equations, substitution method
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