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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.
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.
Let's represent the current stock price as c.
To find an expression that represents the current stock price, we can add 120% to the previous price, p.
Expression 1:
c = p + (120% of p)
To simplify this expression, we can convert 120% to decimal form by dividing it by 100:
c = p + (1.2 * p)
To further simplify, we can factor out p:
c = (1 + 1.2) * p
Simplifying further, we have:
c = 2.2 * p
Now, let's find the second equivalent expression.
Expression 2:
Since the stock price increased by 120%, we can express the new stock price as 220% (or 2.2 times) of the previous price, p.
c = (220% of p)
Similar to before, we need to convert 220% to decimal form:
c = (2.2 * p)
Hence, the two equivalent expressions for the current stock price (c) are:
1. c = 2.2 * p
2. c = (1 + 1.2) * p
Both of these expressions represent the current stock price and are equivalent. They both take the previous price (p) and multiply it by 2.2, which indicates a 120% increase in the stock price.
To prove their equivalence, let's substitute a value for p and verify that both expressions give the same result.
Let's assume p = $100.
Substituting p = 100 into both expressions:
Expression 1:
c = 2.2 * 100
c = 220
Expression 2:
c = (1 + 1.2) * 100
c = 2.2 * 100
c = 220
As we can see, both expressions yield the same result, verifying their equivalence.