The ratio of seventh grade students to eighth grade students in the school band is 3:4. You are told that there are 36 seventh grade students in the band.

Let's break it down step by step:

1. The ratio of seventh graders to eighth graders is $3:4$.
2. The number of seventh graders is given as 36.

To find out how many eighth graders there are, we set up a proportion based on the ratio:

$\frac{\text{seventh graders}}{\text{eighth graders}} = \frac{3}{4}$

Now, we plug in the number of seventh graders (36) into the equation:

$\frac{36}{x} = \frac{3}{4}$

We solve for $x$ by cross-multiplying:

$36 \times 4 = 3 \times x$

$144 = 3x$

Now, divide both sides by 3 to find $x$:

$x = \frac{144}{3} = 48$

So, there are 48 eighth graders in the band.

Now, to find the total number of students in the school band, we add the number of seventh graders and eighth graders:

$36 + 48 = 84$

Thus, the total number of students in the school band is 84, so the correct answer is:

A. 84

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Would you like more details or have any further questions? Here are five additional questions related to ratios and proportions:

1. If the ratio of boys to girls in a class is 2:3 and there are 24 boys, how many girls are there?
2. In a club, the ratio of adults to children is 5:2. If there are 40 adults, how many children are there?
3. A recipe calls for ingredients in the ratio 4:5. If 40 grams of the first ingredient is used, how much of the second ingredient is needed?
4. The ratio of cats to dogs in a shelter is 7:9. If there are 63 cats, how many dogs are there?
5. A team has a win-loss ratio of 8:3. If they have 32 wins, how many games have they lost?

Tip: Always ensure the total parts of a ratio match the corresponding quantities before applying proportions!