Chapter ISG, Problem 6.3.8P

i.

To determine

To write a system of equation

Answer to Problem 6.3.8P

  $4x+2y=18.50$

  $7x+2y=26.75$

Explanation of Solution

Given information:

Name	Bags of popcorn	Plates of nachos	Total cost
J	4	2	$18.50
K	7	2	$26.75

Calculation:

Let the cost of popcorns be x and nachos be y.

According to question,

  $4x+2y=18.50$  -(1)

  $7x+2y=26.75$  -(2)

These are the system of equations.

ii.

To determine

To solve the system of equations.

Answer to Problem 6.3.8P

Cost of 1 bag of popcorn is $2.75 and cost of 1 plate of nachos is $3.75

Explanation of Solution

Given information:

Name	Bags of popcorn	Plates of nachos	Total cost
J	4	2	$18.50
K	7	2	$26.75

Calculation:

From above,

  $4x+2y=18.50$  -(1)

  $7x+2y=26.75$  -(2)

Taking (1)

  $4x+2y=18.50$

Rearranging,

  $2y=18.50-4x$  -(3)

Put value of $2y$ in (2)

  $7x+18.50-4x=26.75$

Solving,

  $3x=26.75-18.50$

So,

  $3x=8.25$

Dividing equation by 3,

  $x=2.75$

Put value of x in (3)

  $2y=18.50-4(2.75)$

Solving,

  $2y=18.50-11$

So,

  $2y=7.5$

Dividing by 2,

  $y=3.75$

Hence, cost of 1 bag of popcorn is $2.75 and cost of 1 plate of nachos is $3.75