Chapter 5.6, Problem 29PPS

a.

To determine

To calculate: The number of rooms that Sybrina can paint and also can paint all the rooms with two coats.

Answer to Problem 29PPS

The Sybrina can then paint a maximum of two rooms in satin if she paints her room and 1 son’s room in satin, her daughter’s room and 1 son’s room in satin or both son’s rooms in satin. She could also paint 1 room in satin is she just paints her room , just her daughter’s room or just one son’s room in satin.

Explanation of Solution

Given:

The wall area of bedroom= $640\text{ sq}\text{.ft}$

The wall area of her daughter’s bedroom = $470\text{ sq}\text{.ft}$

The wall area of her two son’s bedrooms = $320\text{ sq}\text{.ft}$ each

The cost of paint in some of the rooms in satin= $\$40\text{ per gallon}$ ,

The cost of paint other rooms in flat at $\$20\text{ per gallon}$ .

Total budget = $\$350$ .

Calculation:

Let x be the number of gallons of satin paint and y be the number of gallons of flat paint. Since each gallon of satin paint is $40 and each gallon of flat paint is $20, the total cost will be

  $40x+20y$ . Her budget is $\$350$ so,

  $\begin{array}{c}40+20y\le 350.\\ 20y\le -40x+350.\\ y\le -2x+17.5\end{array}$

If she paint each room with two coats ,she needs enough paint to cover a total of $2\left(640\right)=1280$ square feet in her bedroom , $2\left(470\right)=940$ square feet in her daughter’s bedroom and $2\left(320\right)=640$ squares feet for each of her two son’s bedroom. Each gallon of paint covers $350$ square feet so to find the number of gallons of paint needed the number of square feet of the rooms must be divided by $350$ .

So, she can then paint a maximum of two rooms in satin if she paints her room and 1 son’s room in satin, her daughter’s room and 1 son’s room in satin or both son’s rooms in satin. She could also paint 1 room in satin is she just paints her room , just her daughter’s room or just one son’s room in satin.

b.

To determine

To write the assumption made to solve this problem.

Answer to Problem 29PPS

One assumption made was that the paint could only be purchased in whole number gallons.

A second assumption was that the paint was the same color for each finish of satin and flat.

A third assumption was that at least one room had to be painted in satin.

Explanation of Solution

Given:

The wall area of bedroom= $640\text{ sq}\text{.ft}$

The wall area of her daughter’s bedroom = $470\text{ sq}\text{.ft}$

The wall area of her two son’s bedrooms = $320\text{ sq}\text{.ft}$ each

The cost of paint in some of the rooms in satin= $\$40\text{ per gallon}$ ,

The cost of paint other rooms in flat at $\$20\text{ per gallon}$ .

Total budget = $\$350$ .

Calculation:

One assumption made was that the paint could only be purchased in whole number gallons. If smaller units of paint could have been purchased. Such as pints or quarts, the paint needed would have been smaller and cheaper to buy.

A second assumption was that the paint was the same color for each finish of satin and flat. If the rooms were to be painted different colors, the number of gallons of paint would be higher since the same gallon could not be used to finished painting more than one room in the same finish.

A third assumption was that at least one room had to be painted in satin since the problem stated she wanted to paint some rooms in satin .If all the rooms could have been painted in a flat finish ,there would have been ab additional solution.