SOLUTION: I would like to receive help on this question: 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 a

Question 371767: I would like to receive help on this question:
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?

I dont really know how to set this word problem up, and I'd be great if you explained it to me.
Thanks:)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Since one is gaining and the other is losing, there will be a day when they both
weigh the same;
Let d = the number of dieting days for this happen.
:
Frank gains 2 lb a day or a total of 2d lbs
John loses 3 lb a day for a total of 3d lbs
:
An equation for this:
:
John's weight = Frank's weight
208 - 3d = 160 + 2d
do some basic algebra
208 - 160 = 2d + 3d
48 = 5d
d =
d = 9.6 dieting days, they will weight the same
:
How much will they weigh?
:
Using John's equation
weight = 208 - 3(9.6)
w = 208 - 28.8
w = 179.2 lbs
:
Check this using Frank's equation (should be the same if we did it right)
w = 160 + 2(9.6)
w = 160 + 19.2
w = 179.2 lbs
:
:
How about this? Did I make it understandable to you?
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