I need the answer to this word problem

Question

A person invested $30 comma 000 in stocks and bonds. Her investment in bonds is $3000 more than half her investment in stocks. How much did she invest in stocks? How much did she invest in bonds?

Answer 1

Hi Lia, to answer this question we need to set up a system of equations and use substitution to solve. The two equations we have are:

 

(Stocks) + (Bonds) = 30,000

(Bonds) = 3,000 + 0.5 x (Stocks)

 

Next, we rewrite the first equation to be:

(Stocks) = 30,000 - (Bonds)

 

Finally, we substitute and solve:

(Bonds) = 3,000 + 0.5 x (30,000 - Bonds)

(Bonds) = 3,000 + 15,000 - 0.5(Bonds)

1.5 (Bonds) = 18,000

(Bonds) = 12,000

(Stocks) = 18,000

 

So, she invested $12,000 in bonds and $18,000 in stocks