A grain of sand has a mass of [tex]6.66 \times 10^x[/tex] grams, and a grain of salt has a mass of [tex]5.85 \times 10^y[/tex] grams. What is the total mass of two grains of sand and five grains of salt?

Write your answer using scientific notation and round the coefficient to the nearest hundredth as necessary.

To find the total mass of two grains of sand and five grains of salt, we can follow a series of simple calculations. Here’s a step-by-step explanation:

1. Calculate the total mass of two grains of sand:
- A single grain of sand has a mass of [tex]$6.66 \times 10$[/tex] grams.
- Therefore, the mass of two grains of sand is:
[tex]\[
2 \times 6.66 \times 10 = 133.2 \text{ grams}
\][/tex]

2. Calculate the total mass of five grains of salt:
- A single grain of salt has a mass of [tex]$5.85 \times 10$[/tex] grams.
- Therefore, the mass of five grains of salt is:
[tex]\[
5 \times 5.85 \times 10 = 292.5 \text{ grams}
\][/tex]

3. Calculate the total combined mass:
- Add the mass of the two grains of sand to the mass of the five grains of salt:
[tex]\[
133.2 + 292.5 = 425.7 \text{ grams}
\][/tex]

4. Express the total mass in scientific notation:
- The total mass of 425.7 grams can be written in scientific notation. Rounding the coefficient to the nearest hundredth, we get:
[tex]\[
4.26 \times 10^2 \text{ grams}
\][/tex]

Therefore, the total mass of two grains of sand and five grains of salt is [tex]$4.26 \times 10^2$[/tex] grams.