Jake will need to lose 2.1 lbs weekly.
Tawa will need to gain 1 lbs weekly.
The goals are reasonable and fall within the 1.5 % per week body weight restriction.
Each boy needs to gain or lose a set amount of weight each week for a period of 6 weeks to meet a target weight of 182 pounds. Let's start by organizing some information.
Information Needed
Jake
Tawa
Current Weight (lbs.)
194.6
176
Total Change in Weight Needed (lbs.)
-12.6
6
To find how much weight each boy will need to gain or lose per week, we divide the total needed change by the number of weeks.
Jake:&& -12.6 lbs/6 weeks &= -2.1 lbs/weeks
Tawa:&& 6 lbs/6 weeks &= 1 lbs/weeksNow that we know how much each boy needs to gain or lose per week, we need to see if this is a healthy amount of change. We do this by finding 1.5 % of each boy's weight for each week, assuming that they have lost exactly the desired amount. Let's think about the first week.
Jake:&& 194.6 ( 0.015) &= 2.919 lbs
Tawa:&& 176 ( 0.015) &= 2.64 lbs
The change in each boy's weight will be within 1.5 % making each regiment reasonable for the first week. We will also need to check each of the remaining five weeks.
Jake
Recall that we calculated that Jake's weight would reduce by 2.1 lbs weekly.
Week
Starting Weight for the Week
Weight *0.015
1.5 %
Is 2.1 less than 1.5 %?
1
194.6
194.6 *0.015
2.919
Yes
2
194.6-2.1= 192.5
192.5 *0.015
2.8875
Yes
3
192.5-2.1= 190.4
190.4 *0.015
2.856
Yes
4
190.4-2.1=188.3
188.3 *0.015
2.8245
Yes
5
188.3-2.1=186.2
186.2 *0.015
2.793
Yes
6
186.2-2.1=184.1
184.1 *0.015
2.7615
Yes
As we can see in the table, each week Jake is allowed to lose more than 2.1 lbs every week and still remain within the realm of healthy changes. Therefore, we can say that the regiment is acceptable for Jake.
Tawa
Note that we calculated that Tawa's weight would increase by 1 lbs weekly.
Week
Starting Weight
Weight *0.015
1.5 %
Is 1 less than 1.5 %?
1
176
176 *0.015
2.64
Yes
2
176+1=177
177 *0.015
2.655
Yes
3
177+1=178
178 *0.015
2.67
Yes
4
178+1=179
179 *0.015
2.685
Yes
5
179+1=180
180 *0.015
2.7
Yes
6
180+1=181
181*0.015
2.715
Yes
As we can see in the table, Tawa is allowed to gain more than 1 lb each week and still remain in the healthy range of weight fluctuations. Therefore, we can say that the regiment is also acceptable for Tawa.
