Question

a developmental ceramic is designed to be 35 percent silica and 65 percent sulfur if a researcher needs 75g of this material how may grams of each component will she need

Answer 1

To determine the grams of each component needed for the developmental ceramic, set up a system of equations using the given percentages and total mass. Solve the system to find that the researcher will need 21 grams of silica and 54 grams of sulfur.

Step-by-step explanation:

To determine the grams of each component needed for the developmental ceramic, we can set up a system of equations using the given percentages and total mass.

Let x represent the grams of silica and y represent the grams of sulfur. We can set up the following equations:

x + y = 75 (equation 1)

(35/100)x + (65/100)y = 75 (equation 2)

Multiplying equation 2 by 100 to get rid of the decimals, we have:

35x + 65y = 7500 (equation 3)

Now we can solve equations 1 and 3 as a system of linear equations to find the values of x and y:

35x + 65y = 7500

x + y = 75

Solving this system, we find x = 21 g and y = 54 g.

Therefore, the researcher will need 21 grams of silica and 54 grams of sulfur.