Chapter 5.3, Problem 28E

a.

To determine

To estimate number of students

Answer to Problem 28E

The number of students are 25

Explanation of Solution

Given information:

Total number of students are 50

Calculation:

According to question, out of 50, 25 chose dinner.

So,

Number of students with breakfast and lunch= $50-25$

Hence, number of students are 25.

b.

To determine

To write a system of linear equation

Answer to Problem 28E

  $y=x+5$

Explanation of Solution

Given information:

Number of students = 50

Calculation:

Let the number of students choosing breakfast be x and number of students choosing lunch be y .

According to question,

  $y=x+5$

Hence, this is the system of equation.

c.

To determine

To solve the system of equation

Answer to Problem 28E

  $y=15,x=10$ is solution of the system of equation.

Explanation of Solution

Given information:

Number of students = 50

Calculation:

According to question,

  $x+y+25=50$

Solving,

  $x+y=50-25$

So,

  $x+y=50-25$(1)

Also, from part b,

  $y=x+5$(2)

Taking (2),

  $y=x+5$

Put y in (1),

  $x+x+5=25$

Solving,

  $2x=25-5$

Dividing by 5,

  $x=\frac{20}{2}$

So,

  $x=10$

Put x in (2),

  $y=10+5$

Hence,

  $y=15,x=10$ is solution of the system of equation.