Answer :
From the question, we have that:
1. Chang had $10,000 to invest.
2. Let x the part Chang invested in an account that paid 5% simple interest per year.
3. Let y the part Chang invested in an account that paid 8% simple interest per year.
4. After one year, he received $740 in interest.
Then we can translate the situation as follows:
[tex]\begin{gathered} \frac{5}{100}x+\frac{8}{100}y=740 \\ \\ x+y=10000 \end{gathered}[/tex]And we can solve this system using the substitution method to find x and y as follows:
6. We can multiply the first equation by 100 as follows:
[tex]\begin{gathered} 100(\frac{5}{100}x+\frac{8}{100}y)=100*740 \\ \\ 5x+8y=74000 \end{gathered}[/tex]7. Substituting y in terms of x, we have:
[tex]\begin{gathered} x+y=10000\Rightarrow y=10000-x \\ \\ 5x+8y=74000 \\ \\ 5x+8(10000-x)=74000 \end{gathered}[/tex]8. Using the distributive property, we have:
[tex]\begin{gathered} 5x+80000-8x=74000 \\ 5x-8x=74000-80000 \\ -3x=-6000 \\ x=\frac{-6000}{-3} \\ x=2000 \end{gathered}[/tex]Therefore, x = $2000, and knowing that:
[tex]\begin{gathered} x+y=10000 \\ 2000+y=10000 \\ y=10000-2000 \\ y=8000 \end{gathered}[/tex]If we apply one of the above expressions, we have:
[tex]\begin{gathered} \frac{5}{100}x+\frac{8}{100}y=740 \\ \\ \frac{5}{100}2000+\frac{8}{100}8000=740 \\ \\ 740=740 \end{gathered}[/tex]Therefore, in summary, Chang invested $2000 at 5% of simple interest, and $8000 at 8%. He invested
First account (5%) = $2000.
Second account (8%) = $8000.
