Chapter ISG, Problem 6.2.2P

a.

To determine

To write an equation

Answer to Problem 6.2.2P

  $3(x+21)+17=y$

Explanation of Solution

Given information:

	Big cats	Petting zoo
Adults	x	21
Children	1024	y

Calculation:

Let total number of adults be $(x+21)$ .

According to question,

  $3(x+21)+17=y$  -(1)

This is the equation modelled.

b.

To determine

To write an equation

Answer to Problem 6.2.2P

  $(1024+y)+681=10(x)$

Explanation of Solution

Given information:

	Big cats	Petting zoo
Adults	x	21
Children	1024	y

Calculation:

Let total number of children be $1024+y$

According to question,

  $(1024+y)+681=10(x)$   -(2)

c.

To determine

To solve the system of equations

Answer to Problem 6.2.2P

Total number of adults= $x+21$ =255+21=268

Total number of children= $1024+y$ =1024+845=1869

Explanation of Solution

Given information:

  $\begin{array}{l}3(x+21)+17=y\\ (1024+y)+681=10(x)\end{array}$

Calculation:

Let the both equations be (1) and (2)

Taking (1)

  $3(x+21)+17=y$  -(3)

Substituting value of y in (2),

  $(1024+3(x+21)+17)+681=10(x)$

Solving equation,

  $1024+3x+63+17+681=10x$

Rearranging equation,

  $1024+681+63+17=10x-3x$

So,

  $7x=1785$

And,

  $x=255$  -(4)

Put value of $x$ in (3)

  $3(255+21)+17=y$

Solving,

  $828+17=y$

So,

  $y=845$

d.

To determine

To solve the system of equations

Answer to Problem 6.2.2P

Adults, $x=530$

Children, $y=3450$

Explanation of Solution

Given information:

Cost of adult ticket=$25

Cost of children ticket=$10

Total revenue collected=$47750

Calculation:

Let’s assume number of adults be x and number of children be y

According to question,

  $25x+10y=47750$   -(5)

Also,

  $y-270=6x$  -(6)

For solutions,

Taking (6)

  $y-270=6x$

Rearranging

  $y=6x+270$  -(7)

Put value of y in (5)

  $25x+10(6x+270)=47750$

Solving equation,

  $25x+60x+2700=47750$

So,

  $85x=47750-2700$

And,

  $85x=45050$

Dividing equation by 85,

  $x=530$

Put value of x in (7)

  $y=6(530)+270$

Solving equation,

  $y=3450$

Hence, $x=530$ and $y=3450$