Stocks and bonds

Mr. Cash invested $80000 in various stocks and bonds. He earned a 7% dividend on his stocks and 5% interest on his bonds, for a one year profit (both stocks and bonds) of $4,900. How much did Mr. cash invest in bonds?

Correct answer:

b =  35000 USD

Step-by-step explanation:

$$\begin{gathered} x=80000\text{USD} \\ {r}_1=7\%=\frac{7}{100}=0.07 \\ {r}_2=5\%=\frac{5}{100}=\frac{1}{20}=0.05 \\ p=4900\text{USD} \\ x=a+b \\ {r}_1\cdot a+r_2\cdot b=p \\ 80000=a+b \\ 0.07\cdot a+0.05\cdot b=4900 \\ a+b=80000 \\ 0.07a+0.05b=4900 \\ Row2-0.069999999999709\cdot Row1\to Row2 \\ a+b=80000 \\ -0.02b=-700 \\ b=\frac{-699.99999998}{-0.02}=34999.99999966 \\ a=80000-b=80000-34999.99999966=45000.00000034 \\ a=45000 \\ b=35000=35000\text{USD} \end{gathered}$$

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