4 Gears A and B turn together. Gear A turns 20 times when
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Let x be the number of weeks; therefore, the two linear equations are
Where T stands for the punches on the tea punch card and C for the punches on the coffee punch card.
Solving by substitution. Set T=C, then
Thus, substitute the value of x=3 into the first equation,
Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.