Mike makes his trail mix with a 5 : 3 ratio of peanuts to raisins. Dorothy prefers her trail mix to have a 2 : 1 peanut-to-raisin ratio. How many ounces of peanuts should Dorothy add to 24 ounces of Mike's trail mix to get her desired ratio? Please help and thank you!

x = - 36

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = ← k is the constant of variation

To find k use the condition y = 27 when x = 12, then

k = yx = 27 × 12 = 324, thus

y = ← is the equation of variation

When y = - 9, then

- 9 = ( multiply both sides by x )

- 9x = 324 ( divide both sides by - 9 )

x = - 36