5a + 5b + 5c = −20 4a + 3b + 3c = −6 −4a + 3b + 3c = 9
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Answer:
Step-by-step explanation:
Let's write the left hand side as a negative power, and 9 as a power of 3:
At this point, for the equality to still stand, the exponents have to be equal:
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.