ACT review: The length of a rectangle is 3 times the length of a smaller rectangle.

[cbridgeman]

The answer to this first question is 3. I am having trouble setting up the equation.

1. The length of a rectangle is 3 times the length of a smaller rectangle. The 2 have the same widths. The area of the smaller is A sq. units and the area of the larger is kA sq. units. What is the value of k?

The answer to the second question is 3:2:1. I don't know if I should add the 2 fractions then subtract from 1?

2. Jay, Kevin, & Seth shared a sub sandwich. Jay ate 1/2 of it. Kevin ate 1/3 of it and Seth ate the rest. What is the ratio of Jay's share, to Kevin's, to Seth's ?

 

[stapel]

1. The length of a rectangle is 3 times the length of a smaller rectangle. The 2 have the same widths. The area of the smaller is A sq. units and the area of the larger is kA sq. units. What is the value of k?

The answer to this first question is 3. I am having trouble setting up the equation.

What have you tried?

You made a drawing, showing two rectangles of the same height (for "width"), and with the larger one about three times as long as the smaller one. You labelled the height for each as "h". You labelled the width for the small one as "w" and the large one as "3w". You created the "area" expressions for each, and set them equal to the given "area" expressions. And... then what?

2. Jay, Kevin, & Seth shared a sub sandwich. Jay ate 1/2 of it. Kevin ate 1/3 of it and Seth ate the rest. What is the ratio of Jay's share, to Kevin's, to Seth's?

The answer to the second question is 3:2:1. I don't know if I should add the 2 fractions then subtract from 1?

If you mean that, to find Seth's portion, you want to add Jay's and Kevin's portions, and then subtract their total from "1" (for "one whole") then, yes, this is a valid step. Then convert each person's share to a fraction, with a common denominator. Then you'll have the ratios right.

If you get stuck, please reply with a clear listing of your efforts so far. Thank you!

 

[cbridgeman]

I did not get my 3 fractions to have a common denominator. Thank you!!

All is have so far on my first question is the drawings with the correct labels. I am stumped after that.

 

[stapel]

All is have so far on my first question is the drawings with the correct labels. I am stumped after that.

So, given a rectangle with labelled dimensions, you don't know how to find the area? :shock:

To learn about basic geometric formulas, such as areas of rectangles, please try Google.