Answer:
[tex]Y = 7\frac{1}{2}[/tex]
Step-by-step explanation:
Missing Table:
Yellow Paint ----------- Red Paint
5 ---------------------------------6
Required
Determine the quarts of yellow paints when 9 quarts of red are used
Represent Yellow with Y and Red with R.
When Y = 5 and R = 6, we have the following:
[tex]Y : R = 5 : 6[/tex]
Represent as a fraction
[tex]\frac{Y}{R} = \frac{5}{6}[/tex]
When R = 9 and Y is unknown, we have the following:
and
[tex]Y : R = Y : 9[/tex]
Represent as a fraction
[tex]\frac{Y}{R} = \frac{Y}{9}[/tex]
Since the given parameters re[resent a direct variation between both paints, we can equate both fractions to solve for Y
[tex]\frac{5}{6} = \frac{Y}{9}[/tex]
Multiply through by 9
[tex]9 * \frac{5}{6} = \frac{Y}{9} * 9[/tex]
[tex]9 * \frac{5}{6} = Y[/tex]
[tex]3 * \frac{5}{2} = Y[/tex]
[tex]\frac{15}{2} = Y[/tex]
[tex]7\frac{1}{2} = Y[/tex]
[tex]Y = 7\frac{1}{2}[/tex]
Hence, [tex]7\frac{1}{2}[/tex] quarts of the yellow paints is required
