Ryan invests M dollars in the stock market. After his investment increases by 10%, he takes out \$150 and sets it aside. The remaining investment then decreases by 10%. If the sum of the invested money and the \$150 set aside are 4% larger than the original investment M, by what dollar amount has M increased?
Investments in M -HomeWork
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algebra-precalculus
1 Answers
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Initial amount is $M$.
After investment increases by $10 \%$, the amount is $1.1M$.
He takes out $150$ and hence the amount now is $1.1M - 150$.
The remaining amount decreases by $10 \% \implies$ the amount is $0.9 (1.1M - 150) = 0.99 M - 135$
The sum of this and $150$ is $4\%$ larger than the initial amount i.e. $0.99 M - 135 + 150 = 1.04 M \implies0.05M = 15 \implies M = 20 \times 15 = 300$
Hence, the initial amount invested is $\$ 300$.