CPhill

1) Given the proportion a/b = 11/20 , what ratio completes the equivalent proportion a/11 = ? (The answer needs to be a fraction)

Notice something, RP

If

5/10   =  1/2        then it is also true that  the ratio of the numerators to the ratio of the denominators is the same....that is :

5/1  =  10/2

This implies   that

a /b   =  11/20      means that

a / 11  =  b / 20

Do you see this??

2) A model is made of a car. The car is 3 meters long and the model is 4 centimeters long. What is the ratio of the length of the car to the length of the model?

Equate units in terms of centimeters

3 m  =   300  cm

Ratio  :   actual length  / model length   =    300 cm / 4 cm   =   75 / 1   =  75 : 1

6  is correct for the second one  !!!

OK....for the last....you have it set up correctly

5(3y - 8)  =  12y    simplify

15y - 40   =  12y      subtract  15y   from both sides

-40  =   -  3y        divie both sides by  - 3

40/3   =  y

HAHAHA!!!!....don't know about that...but...I do know a few answers, here and there...

We can solve everyone of these by cross-multiplication...so

6/a  =  18 /24      cross-multiply

24 * 6  =  18 * a

144  =  18 *a      divide both sides by   18

8  =  a

I'll  do  the third one....you try the other two, RP....let me know if you get stuck

n - 6 / 3n  =  n - 5 / 3n + 1        cross-multiply

(n - 6) (3n + 1)  =  3n ( n - 5)      simplify

3n^2 - 18n + 1n - 6  =  3n^2 -  15n      subtract 3n^2  from both sides

-17n - 6  =  - 15n       add  17n  to both sides

-6   =  2n      divide both sides by 2

-3  =  n

No....I just did that for convenience, Manuel....your solutions are correct  !!!

6. A salsa recipe uses green pepper, onion, and tomato in the extended ratio 2 : 5 : 8. How many cups of onion are needed to make 105 cups of salsa?

There are   2 + 5 + 8   =   15  parts.....and  the onion  is  (5/15)  = 1/3

So.....  105 (1/3)   =  35  cups of onion

7. The measures of the angles of a triangle are in the extended ratio 2 : 3 : 5. What is the measure of the smallest angle?

There are  2 + 3 + 5    =  10  parts.....

And the smallest angle is  2/10  of this

So.....(2/10) 180   =  2 * 180 / 10   =  2 * 18   =   36°

4. The measure of two complementary angles are in the ratio 1 : 5. What are the degree measures of the two angles?

1 : 5  means there are 6 equal parts....

So...one  of them  is  (1/6) of these

So     (1/6) * 90   =   15°

And   (5/6) * 90   =  5 * 15   =  75°

5. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 56 feet, what is the length of the rectangle?

P  =  2 (L + W)      but  L  =  3W.....so we have...

56   =  2 ( 3W + W)     divide by 2

28  =  3W + W

28  =  4W     divide by 4

7 = W

So  L  =  3W  =  3(7)   =  21 ft

        x^2 - 6x + 8            x  - 2

x

0            8                        -2

1            3                        -1 

2            0                         0     

3            -1                        1

4             0                        2

5             3                        3  

The solutions  are  in red  ⇒  x  =  2   and x  =  5

5 : 2    means that there are  5 + 2  =  7 equal parts

And  the red bricks  are   5/7  of the total....so.....

(5/7) 210  =

5 (210 / 7)  =

5 (30)  =

150   red bricks

And

The grey bricks  are 2/7  of the total  =

(2/7) (210)  =

2 ( 210 / 7)  =

2 (30)  =

60  grey bricks

As Julius found

y  =  8 / x

This is  a  hyperbola