Mathematics: The table shows of a ratio used to make of orange paint use a table how many quarts of yellow paint would be required to make the shade of orange if you use 9 quarts of red paint

The table shows of a ratio used to make of orange

Need1ng

11.02.2022

$Y = 7\frac{1}{2}$

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:

Y : R = 5 : 6

Represent as a fraction

$\frac{Y}{R} = \frac{5}{6}$

When R = 9 and Y is unknown, we have the following:

and

Y : R = Y : 9

Represent as a fraction

$\frac{Y}{R} = \frac{Y}{9}$

Since the given parameters re[resent a direct variation between both paints, we can equate both fractions to solve for Y

$\frac{5}{6} = \frac{Y}{9}$

Multiply through by 9

$9 * \frac{5}{6} = \frac{Y}{9} * 9$

$9 * \frac{5}{6} = Y$

$3 * \frac{5}{2} = Y$

$\frac{15}{2} = Y$

$7\frac{1}{2} = Y$

$Y = 7\frac{1}{2}$

Hence, $7\frac{1}{2}$ quarts of the yellow paints is required

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