Question

PAINT FORMULA

White: $\frac{3}{5}$ gallon Red : $\frac{1}{4}$ gallon Yellow :$\frac{1}{3}$ gallon

A paint store makes peach paint according to the formula above. The numbers of gallons of white and yellow paint used in a batch of peach paint are always each an integer. If the store owner wants to make the smallest batch of peach paint possible, how many gallons of red are needed ?

• A. $\frac{1}{4}$
• B. $1$
• C. $3\frac{3}{4}$
• D. $5$

Answer 1

The correct option is C $3\frac{3}{4}$

The formula for the peach paint is given as :
White $=\frac{3}{5}$ gallon
Red $=\frac{1}{4}$ gallon
Yellow $=\frac{1}{3}$ gallon
That means in this ratio it can be mixed always to make peach paint.
Now the question says the volume of white and yellow paint must be an integer.

So we have to take LCM of $5$ and $3$ to make both volumes of white and yellow paint an integer.

Minimum multiplication factor is $15$.

Therefore White Paint $=\frac{3}{5}\times 15=9$ gallon and yellow Paint $=\frac{1}{3}\times 15=5$ gallon.

Red paint can be in decimal.

So red paint $=\frac{1}{4}\times 15=3\frac{3}{4}$ gallon.