Chapter SH, Problem 6.18EP

a.

To determine

To write system of equation to represent situation.

Answer to Problem 6.18EP

  $10x+4y=52$

  $15x+2.5y=67.50$

Explanation of Solution

Given information:

  

K made $52 by charging $10 per hour and $4 per child.

E made $67.50 by charging $15 per hour and $2.50 per child.

Calculation:

Let both babysit x hour individually

Let both babysit y child individually

Then sysem of equations

  $10x+4y=52$

  $15x+2.5y=67.50$

b.

To determine

To calculate how many hour and how many child did each babysit.

Answer to Problem 6.18EP

Each babysit work 4 hours

Babysit 21 childs

Explanation of Solution

Given information:

  

K made $52 by charging $10 per hour and $4 per child.

E made $67.50 by charging $15 per hour and $2.50 per child.

Calculation:

Let both babysit x hour individually

Let both babysit y child individually

Then, according to given sysem of equations

  $10x+4y=52\mathrm{............}(1)$

  $15x+2.5y=67.50\mathrm{...........}(2)$

Multiply equation (1) by 3 and equation (2) by 2

  $30x+12y=156\mathrm{............}(3)$

  $30x+5y=135\mathrm{...........}(4)$

Substracting (4) from (3),

  $7y=21$

On solving,

  $y=3$

Substituting $y=3$in equation (1)

  $10x+4(3)=52$

On solving,

  $10x+12=52$

On solving,

  $10x=40$

Then, x=4

Hence, each babysit work 4 hours and 21 child.