Amixture contains 1/16 pound sand and 7/8 pound compost. at that rate, what amount of sand is needed if the mixture contains 1 pound of compost? a. 1/14pound b. 8/24pound c. 14 pounds d. 15/16pound

A. ¹/₁₄ lb  

Step-by-step explanation:

¹/₁₆ lb sand goes with ⅞ lb compost.

For 1 lb compost, the mass of sand needed is:

1 lb compost × (¹/₁₆ lb sand)/(⅞ lb compost).

We must evaluate the fraction (¹/₁₆)/(⅞).

Invert the denominator and multiply

(¹/₁₆)/(⅞) = ¹/₁₆ × ⁸/₇             Cancel the 8s

                      = ½ × ⅐      Multiply numerators and denominators

                      = ¹/₁₄

For 1 lb of compost, the mass of sand needed is ¹/₁₄ lb.

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3