To solve the problem, we need to analyze the two types of molten metals involved in the mixture and how they contribute to the total amount of silver in grams.
Let’s break down the expressions given:
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(15)(0.75): This expression represents 75% of the total weight (15 grams) from one of the metals. So, it calculates the grams of silver from that metal alone: \[ (15)(0.75) = 11.25 \text{ grams of silver} \]
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0.7(15 - x) + 0.9x: Here, \(x\) represents the amount (in grams) of the second molten metal containing 90% silver, while \(15 - x\) is the amount of the first metal containing 70% silver. The expression calculates the total grams of silver contributed by both metals:
- The first metal contributes \(0.7(15 - x)\)
- The second metal contributes \(0.9x\) Hence, the total silver is: \[ 0.7(15 - x) + 0.9x \]
Now, let's look at the options provided:
- (15)(0.75) and 0.7(15 – x) + 0.9x
- (15)(0.75) and 0.7(15 – x)(0.9x)
- 15 + 0.75 and 0.7(15 – x) + 0.9x
- 15 + 0.75 and 0.7(15 – x)(0.9x)
The first option, (15)(0.75) and 0.7(15 – x) + 0.9x, includes the correctly calculated amounts of silver from both metals, making it one potential correct expression for the total grams of silver.
The remaining options do not properly represent the calculation of total grams of silver when compared to the expressions derived above.
Thus, the two expressions that are equivalent to \(t\), the total number of grams of silver in the mixture, are:
\[ \boxed{(15)(0.75) \text{ and } 0.7(15 – x) + 0.9x} \]
1 answer