Two equivalent expressions that represent the current stock price of Ever Rise Corporation are:
1. 2.2p (or p + 1.2p): This expression means that the current stock price is 220% of the original price (p). Multiplying p by 1.2 (or adding 1.2p to p) gives us the amount of increase in price, and adding this amount to the original price gives us the new price.
2. 3p (or 2p + p): This expression means that the current stock price is three times the original price (p). If we start with p and increase it by 120%, we get 2.2p. Now, if we increase 2.2p by another 100%, we get 3p.
To prove their equivalence, we can substitute p = 100 (assume the original price was $100) into both expressions:
1. 2.2p = 2.2(100) = 220
p + 1.2p = 100 + 120 = 220
2. 3p = 3(100) = 300
2p + p = 200 + 100 = 300
Both expressions give us the same result (current stock price = $220 or $300), which proves their equivalence.
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Avery owns stocks in Ever Rise Corporation. The stock price increased by 120% over the past week. If the stock price was p last week, write two equivalent expressions that represent the current stock price and explain what their equivalence means. Substitute one or more variables into the expressions to prove them equivalent.
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