Question

Create a system of equation.

Answer 1

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;

$10(y+z)+15(2z)+40z=600$

We know that y=2z from Eqn 2,

$10(2z+z)+30z+40z=600\\20z+10z+70z=600\\100z=600$

Dividing both sides by 100;

$\frac{100z}{100}=\frac{600}{100}\\z=6$

Putting z=6 in Eqn 2;

$y=2(6)\\y=12$

Putting value of y and z in Eqn 1;

$x=12+6\\x=18$

They must sell 18 small pizzas, 12 medium pizzas and 6 small pizzas.

Keywords: linear equations, substitution method

Learn more about linear equations at:

• brainly.com/question/2869849
• brainly.com/question/2920401

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