Level d:

rollie was successful in losing weight. he had a goal

weight in mind. he went on a diet for three months. each

month, he would lose one-third of the difference between

his current weight and his goal weight and an additional

three pounds. at the end of three months, he was just 3

pounds over his goal weight. how many pounds did he

lose in those three months?

explain how you arrived at your solution.

If X is the starting weight, total pounds lost in three months is

(0.132X + 2.37)lbs

Step-by-step explanation:

Let the starting weight be X(lb)

Let the target ending weight be Y(lb)

Since Rollie ended with 3(lbs) above goal weight, final weight is Y+3(lb)

Each month, Rollie lost 1/3 of the difference between current weight and goal weight, hence

In the first month, Rollie lost 1/3 of (X - Y)

but since Rollie ended up with 3lbs above target ending weight, the actual weight loss is 1/3(X - Y) + 3

Hence  by the end of the first month, Rollie's new weight is X - (1/3(X - Y)) + 3

which is equal to

X - 1/3X + 1/3Y - 3.

= 2/3X + 1/3Y - 3

By the second month, Rollie's starting weight is 2/3X + 1/3Y - 3(lb)

while her target ending weight still remains (Y)

but the actual ending weight is Y + 3

hence in the second month, Rollie lost 1/3(2/3X + 1/3Y - 3 - Y) + 3

= 2/9X + 1/9Y - 1 - 1/3Y + 3

=  2/9X - 2/9Y + 2

hence by the end of the second month, Rollie's new weight is

(2/3X + 1/3Y - 3) - (2/9X - 2/9Y + 2)

= 2/3X - 2/9X + 1/3Y + 2/9Y - 3 - 2

= 4/9X + 5/9Y - 5  

By the third month, Rollie's starting weight is 4/9X + 5/9Y - 5(lb)

while her target ending weight still remains (Y)

but the actual ending weight is Y + 3

hence in the third month, Rollie lost 1/3(4/9X + 5/9Y - 5 - Y) + 3

= 4/27X + 5/27Y - 5/3 - 1/3Y + 3

= 4/27X - 4/27Y + 4/3 eqn (*)

hence by the end of the third month, Rollie's new weight is

(4/9X + 5/9Y - 5) - (4/27X - 4/27Y + 4/3)

= 4/9X - 4/27X + 5/9Y + 4/27Y - 5 - 4/3

= 8/27X - 19/27Y - 19/3

Hence in three months, Rollie's new weight is 8/27X - 19/27Y - 19/3

To ascertain how much weight Rollie lost in three months, there is need to equate the estimated ending weight to the final weight (Y + 3)

Therefore:

8/27X - 19/27Y - 19/3 = Y + 3

this implies that

8/27X - 19/27Y - Y - 19/3 - 3 = 0

8/27X - 36/27Y -28/3 = 0

Since Y is the target ending weight

the ending weight is generated by solving the equation with respect to Y

36/27Y = 8/27X - 28/3

multiply through by 27/36

Y = 2/9X - 7

Hence weight lost in three months is generated by substituting for Y = 2/9X - 7  in eqn (*)

Since eqn * is 4/27X - 4/27Y + 4/3

the lbs lost in three months is

4/27X - 4/27(2/9X - 7 ) + 4/3

= 4/27X - 8/243X + 28/27 + 4/3

= (32/243)X + 64/27

which in decimal is

(0.132X + 2.37)lbs

50.6

step-by-step explanation:

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.