A shade of green paint called Groovy Green is made by combining yellow paint and blue paint so that the ratio, by volume, of yellow paint to blue paint is 12 to 5. How many tablespoons of blue paint are needed to make 34 cups of Groovy Green? ( 1 cup= 16 tablespoons)

It will take 160 tablespoons of blue paint

Explanation:  The ratio 12:5 indicates that there are 17 "parts" in the mixture. (Add 12+5 to get that.)

the Blue portion will be 5/17 of the total amount.

The total required is 34 cups, at 16 Tablespoons per cup, for a total of 544 tablespoons.

5/17 of 544 is 160

To check,  The yellow would be 12/17 × 544 = 384

384 + 160 + 544, the correct amount required

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