Question

a metalsmith is mixing two molten metals, each containing different percentages of silver. the table shows the amount of each molten metal used. silver total mass (g) silver percent total 70% silver 15 - x 0.70 0.7(15 - x) 90% silver x 0.90 0.9x mixture 15 0.75 t which two expressions are both equivalent to t, the total number of grams of silver in the mixture? (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)

Explanation:

Step1: Calculate total silver from mixture

The mixture has a total mass of 15 g and a silver percent of 0.75. So, the total silver \( t \) from the mixture is \( (15)(0.75) \).

Step2: Calculate total silver from components

The 70% silver metal contributes \( 0.7(15 - x) \) grams of silver, and the 90% silver metal contributes \( 0.9x \) grams of silver. So, the total silver \( t \) from the components is \( 0.7(15 - x)+0.9x \).

Step3: Identify equivalent expressions

We need to find the option where both expressions for \( t \) match the two we calculated. The first option has \( (15)(0.75) \) (from mixture) and \( 0.7(15 - x)+0.9x \) (from components), which are equivalent.

Answer:

(15)(0.75) and \( 0.7(15 - x)+0.9x \) (the first option in the given choices)