In order for josé and marty to compete against each other during the wrestling season next year they need to be in the same weight category. josé weighs 180 pounds and plans to gain 2 pounds per week. marty weighs 249 pounds and plans to lose 1 pound per week. in how many weeks will they weigh the same? (use substitution)

23 weeks

Let j and m represent the weights of the competitors, and let x represent the number of weeks of interest.

José's weight can be described by ...

... j = 180 +2x . . . . . . José weighs 180 and gains 2 lbs per week

Marty's weight can be described by ...

... m = 249 -x . . . . . . Marty weighs 248 and loses 1 lb per week

The competitors will weigh the same when ...

... j = m

... 180 +2x = 249 -x . . . substitute for j and m

... 3x = 69 . . . . . . . . . add x-180

... x = 23 . . . . . . . . . . divide by the coefficient of x

José and Marty will weigh the same after 23 weeks.

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