Questions: George and Mike are mixing paints for an art project. George wants to mix 4 cups of red with 7 cups of green. Mike wants to mix 5 cups of red with 8 cups of green. Arnie says both mixtures will look the same because Mike is just adding 1 cup of each color to George's mixture and adding the same amount to both does not change the mixture. How can you help? Choose the correct answer below. A. Since 32 ≠ 35 the mixtures are different. B. Arnie is correct that since the same number was added to both the mixtures are the same. C. Since 28 ≠ 40 the mixtures are different. D. Since 20 ≠ 56 the mixtures are different.

George and Mike are mixing paints for an art project. George wants to mix 4 cups of red with 7 cups of green. Mike wants to mix 5 cups of red with 8 cups of green. Arnie says both mixtures will look the same because Mike is just adding 1 cup of each color to George's mixture and adding the same amount to both does not change the mixture. How can you help? Choose the correct answer below. A. Since 32 ≠ 35 the mixtures are different. B. Arnie is correct that since the same number was added to both the mixtures are the same. C. Since 28 ≠ 40 the mixtures are different. D. Since 20 ≠ 56 the mixtures are different.
Transcript text: Points: 0 of 1 George and Mike are mixing paints for an art project. George wants to mix 4 cups of red with 7 cups of green. Mike wants to mix 5 cups of red with 8 cups of green. Arnie says both mixtures will look the same because Mike is just adding 1 cup of each color to George's mixture and adding the same amount to both does not change the mixture. How can you help? Choose the correct answer below. A. Since $32 \neq 35$ the mixtures are different. B. Arnie is correct that since the same number was added to both the mixtures are the same. C. Since $28 \neq 40$ the mixtures are different. D. Since $20 \neq 56$ the mixtures are different.
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Solution

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Solution Steps

Step 1: Understand the problem

George's mixture consists of 4 cups of red and 7 cups of green. Mike's mixture consists of 5 cups of red and 8 cups of green. Arnie claims that since Mike is adding 1 cup of red and 1 cup of green to George's mixture, the mixtures will look the same. We need to determine whether Arnie is correct.

Step 2: Compare the ratios of red to green

To determine if the mixtures are the same, we compare the ratios of red to green in both mixtures.

  • George's ratio: \(\frac{4}{7}\)
  • Mike's ratio: \(\frac{5}{8}\)
Step 3: Check if the ratios are equal

We check if \(\frac{4}{7} = \frac{5}{8}\). To do this, we cross-multiply:

\[ 4 \times 8 = 32 \quad \text{and} \quad 5 \times 7 = 35 \]

Since \(32 \neq 35\), the ratios are not equal. Therefore, the mixtures are different.

Final Answer

The correct answer is A. Since \(32 \neq 35\), the mixtures are different.

\(\boxed{\text{A}}\)

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