Question

Allen is horrible at managing his money. For example, he

recently invested $100,000-part of it in a company that
makes "fish-flavored" chicken and the rest in a company
that makes spray-on vitamins. Somehow he managed to earn
a 3% profit on the fish-flavored chicken investment and 1%
profit on the spray-on vitamin deal. If Allen made a profit
of $2,600 from both investments, how much did he invest in
the fish-flavored chicken company?

Answer 1

$80,000

Explanation:

Define the variables:

Let x = "fish-flavored" chicken company investment (in dollars)

Let y = spray-on vitamins company investment (in dollars)

If Allen invested a total of $100,000:

⇒ x + y = 100000

Given:

• 3% profit on "fish-flavored" chicken investment
• 1% profit on pray-on vitamins investment
• Total profit = $2,600

⇒ 0.03x + 0.01y = 2600

Rewrite the first equation to make y the subject:

⇒ y = 100000 - x

Substitute into the second equation and solve for x:

⇒ 0.03x + 0.01(100000 - x) = 2600

⇒ 0.03x + 1000 - 0.01x = 2600

⇒ 0.02x + 1000 = 2600

⇒ 0.02x = 1600

⇒ x = 80000

Therefore, Allen invested $80,000 in the "fish-flavored" chicken company.