Sender: Jennifer
Date: Wed, 16 Dec 1998 14:55:23 -0800

To Whom It May Concern,
I'm having some difficulty with these word problems. Maybe you could help. Thanks.

  1. A matte of uniform width is placed around a painting so that the area of the matted surface is twice the area of the painting. If the outside dimensions of the matte are 40cm and 60cm, find the width of the matte.

  2. The Joneses start out A 1520km car trip to Walker Park. On the first day they cover 960km. On the second day they complete the trip, but a rainstorm causes them reduce their average speed by 10km/h.If the 2-day trip took a total of 20 h, what was the average speed on each day?

  3. Granny stood up at her grandson's wedding reception and announced " My age now is a perfect square and it is equal to the difference between the square of my grandson's father's age and the square of his mother's age. Come to think of it the difference my age and the square of my grandson's age is seven times the age of his mother, my daughter in law." The grandson's wife remarked to her new husband," That means the difference between the squares of our ages is three times the age of your father!" How old was the bride?

  4. The volume of a retangular box 4cm high is 144 cubic cm. If the perimeter of the base is 24cm, find the dimensions of the box.
P.S. the first two questions are the most important ones that need to be solved.

Thanks for your help!!

Hi Jennifer

We don't like to do homework for students but here is a way to approach problem one.
1.Notice that you have a rectangle (the painting) inside a rectangle (the painting and the matte) whose area is 2400 cm^2. Since the area of the matte is twice the area of the painting, the area of the painting is 1/3 of the total area and is thus 800 cm^2. If the width of the matte is x cm then, from the diagram, the height of the painting will be (40 - 2x) cm and its width will be (60 - 2x) cm. You can thus write the area of the painting as (40 - 2x)(60 - 2x). Since this area is 800 square cms you now have the equation (40 - 2x)(60 - 2x) = 800 which you can solve for x. You will find two values of x that satisfy this equation and you need to decide which gives the desired width.

Jack and Penny

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