1. a chemical compound requires 8 ounces of chemical a and 12 ounces of chemical b. a mixture contains 24 ounces of chemical a and 30 ounces of chemical b. how can you fix the mixture to make the chemical compound?
2. in an animal shelter, the ratio of cats to dogs is 5 to 3. there are 25 cats. write and solve a proportion the find the number x of dogs.
8/12 = 2/3
24/36 = 20/30 = 2/3
So, you can see how to adjust either a or b.
5/3 = 25/x
Can you explain how to answer this problem more specifically?
How do I explain the question
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1. To fix the mixture to make the chemical compound, you need to adjust the amounts of chemicals A and B in the mixture. Here's how you can do it:
Step 1: Determine the ratio of chemical A to chemical B required in the compound. In this case, the ratio is 8 ounces of A to 12 ounces of B, which simplifies to 2:3.
Step 2: Calculate the adjustment factor for each chemical. Divide the actual amount of each chemical in the mixture by the desired amount. For chemical A, the adjustment factor is 24/8 = 3. For chemical B, the adjustment factor is 30/12 = 2.5.
Step 3: Multiply each adjustment factor by its respective chemical in the mixture to determine the adjusted amounts. For chemical A, multiply 3 by 24 ounces, which gives you 72 ounces. For chemical B, multiply 2.5 by 30 ounces, which gives you 75 ounces.
So, to make the chemical compound, you need to add 72 ounces of chemical A and 75 ounces of chemical B to the mixture while keeping the proportions correct.
2. To find the number of dogs (x) in the animal shelter, use the given ratio of cats to dogs and the given number of cats. Here's how to set up and solve the proportion:
Step 1: Write the proportion using the given ratio and the variable x for the number of dogs:
5/3 = 25/x
Step 2: Cross-multiply the fractions. Multiply 5 by x and 3 by 25:
5x = 3 * 25
Step 3: Solve for x by dividing both sides of the equation by 5:
x = (3 * 25) / 5
x = 15
Therefore, there are 15 dogs in the animal shelter.