SAT Systems of two linear equations in two variables Practice Question 14 (Medium)

Question bank / Systems of two linear equations in two variables

Math · AlgebraMedium

Kai invested a total of $\$5{,}000$ in two accounts. One account earns $3\%$ simple annual interest and the other earns $5\%$ simple annual interest. After one year, the total interest earned was $\$206$ . How much did Kai invest in the account that earns $5\%$ ?

$\$2{,}200$

$\$2{,}800$

$\$4{,}120$

$\$3{,}000$

Show answer and explanation

Answer: B

Let $x$ be the amount at $3\%$ and $y$ the amount at $5\%$ : $x + y = 5000$ and $0.03x + 0.05y = 206$ . Substitute $x = 5000 - y$ : $150 + 0.02y = 206$ , so $y = 2800$ .

Choice A is the amount invested at $3\%$ .

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