Question

If an equation, Y varies directly as X varies. If Y equals 208 when X equals 13, what is the value of X when Y equals -144?

Answer 1

DIRECT VARIATION

`\mathbb{ANSWER:}`

Step 1: Write the equation of variation

• 
  `\sf y \propto x`
• 
  `\sf y = kx`

Step 2: Solve for k or the constant of proportionality

• 
  `\sf 208 = k(13)`
• 
  `\sf (208)/(13) = (k(13))/(13)`
• 
  `\sf k = 16`

Step 3: Solve for x

• 
  `\sf -144 = 16x`
• 
  `\sf (-144)/(16) = (16x)/(16)`
• 
  `\sf x = \boxed{\sf -9}`

Answer 2

Answer: X = -9

Explanation:

You can set up a ratio to solve this.

208/13 = -144/x

208x=-1872

x = -9