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Frank weighs 160 pounds and is on a diet to gain two pounds a week so that he can make the football team. John weighs 208 pounds and is on a diet to loose three pounds a week so that he can be in the wrestling team in a lower wight class.?. If Frank and John can meet these goals with their diets, when will they weigh the same, and how much will they weigh at that time?

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JeanaShupp

Answer:  If Frank and John can meet these goals with their diets , they will weigh same after 9.6 weeks and they will weigh 179.2 pounds.

Step-by-step explanation:

Let x = Number of weeks.

As per given question ,

Weight of Frank after x weeks = 160+2x (pounds)

Weight of John after x weeks = 208-3x (pounds)

When  Weight of Frank= Weight of John

[tex]\Rightarrow\ 160+2x= 208-3x[/tex]

[tex]\Rightarrow\ 2x+3x= 208-160[/tex]

[tex]\Rightarrow\ 5x= 48\Rightarrow\ x=\dfrac{48}{5}=9.6[/tex]

Weight of Frank after 9.6 weeks = 160+2(9.6) = 179.2 pounds

Weight of John after 9.6 weeks = 208-3(9.6)=179.2 pounds

Hence,  If Frank and John can meet these goals with their diets , they will weigh same after 9.6 weeks and they will weigh 179.2 pounds.

The number of weeks for which frank and John will weigh the same and the weights are;

Number of weeks = 9.6 weeks

Weight = 179.2 pounds

Let the number of weeks which they will weigh the same be x.

  • Frank weighs 160 pounds and is gaining 2 pounds per week. Thus, after x weeks, he will weigh; 160 + 2x

  • John weighs 208 pounds and is on a diet to loose 3 pounds a week. Thus, after x weeks he will weigh; 208 - 3x

For them to weigh the same after x weeks, it means that;

160 + 2x = 208 - 3x

2x + 3x = 208 - 160

5x = 48

x = 48/5

x = 9.6 weeks

Weight after 9.6 weeks is;

Frank; 160 + 2(9.6) = 179. 2 pounds

John; 208 - 3(9.6) = 179.2 pounds

Read more about equalities at; https://brainly.com/question/11408596

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