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The ratio of blue paint to yellow paint in a certain color of green paint is 2.1. A painter wants a total of 14 quarts of green paint Blue paint is

$16.64 per quart and $34.96 per gallon. Buying the least amount needed, how much will it cost to purchase the blue paint in the most economic

way?

Respuesta :

xero099

Answer:

The blue paint with a unit price of [tex]34.96\,\frac{USD}{gal}[/tex] is the most economic option for the painter. (Cost: [tex]x = 8.74\,\frac{USD}{qt}[/tex])

Step-by-step explanation:

Both gallon and quart are capacity units, we must keep in mind that a gallon equals 4 quarts. We need to convert each price in the same units. In this case, we decided to use US dollars per quart as our reference unit. Hence:

Blue paint 1 ([tex]16.64\,\frac{USD}{qt}[/tex])

No unit conversions are needed.

Blue paint 2 ([tex]34.96\,\frac{USD}{gal}[/tex])

We proceed to the following conversion:

[tex]x = 34.96\,\frac{USD}{gal}\times \frac{1\,gal}{4\,qt}[/tex]

[tex]x = 8.74\,\frac{USD}{qt}[/tex]

The blue paint with a unit price of [tex]34.96\,\frac{USD}{gal}[/tex] is the most economic option for the painter. (Cost: [tex]x = 8.74\,\frac{USD}{qt}[/tex])

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