Question

Elena is mixing paint for a modeling kit. To create a certain shade of green, the instructions ask her to mix 1 (2/3) ounces of yellow paint with 2 (1/3 ) ounces of blue paint. If she wishes to use 2 (1/2) ounces of yellow paint while still keeping the colors in the same ratio, how many ounces of blue paint should she use?

a) 2 (1/3)
b) 2 (5/6)
c) 3 (1/6)
d) 3 (1/2)
e. 4

Answer 1

To maintain the ratio of yellow to blue paint, Elena should mix 2 (1/2) ounces of yellow paint with 3 (1/2) ounces of blue paint.

Step-by-step explanation:

Elena needs to keep the same ratio of yellow paint to blue paint for her green shade. The initial instruction was to mix 1 (2/3) ounces of yellow with 2 (1/3) ounces of blue. To find out how much blue paint Elena should use with 2 (1/2) ounces of yellow paint, we first convert the mixed numbers to improper fractions.

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• 1 (2/3) ounces of yellow becomes 5/3 ounces.
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• 2 (1/3) ounces of blue becomes 7/3 ounces.

Now we calculate the ratio of yellow to blue paint:

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• Ratio = (5/3) : (7/3)
• 
  
• The ratio simplifies to 5:7.

To maintain this ratio with 2 (1/2) ounces of yellow, which is 5/2 ounces, we set up a proportion:

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• 5/2 yellow : x blue = 5 yellow : 7 blue
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• The cross multiplication gives us 5x = (7/2)*5
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• Solving for x gives us x = (7/2) * (5/5) = 7/2 = 3 (1/2) ounces

Therefore, Elena should mix 2 (1/2) ounces of yellow paint with 3 (1/2) ounces of blue paint to keep the colors in the same ratio.