aliya deposited half as much money in a savings account earning 2% simple interest as she invested in a…

Explanation:

Step1: Set up variables

Let $x$ be the amount invested in the money - market account. Then the amount invested in the savings account is $\frac{1}{2}x$.

Step2: Calculate the interest from each account

The interest formula for simple - interest is $I = Prt$, where $P$ is the principal amount, $r$ is the interest rate, and $t$ is the time. Since $t = 1$ year, the interest from the savings account $I_1=\frac{1}{2}x\times0.02$ and the interest from the money - market account $I_2=x\times0.031$.

Step3: Set up the total - interest equation

The total interest $I = I_1+I_2$. We know that $I = 262.40$, so $\frac{1}{2}x\times0.02+x\times0.031 = 262.40$. Simplify the left - hand side: $0.01x+0.031x=262.40$. Combine like terms: $0.041x = 262.40$.

Step4: Solve for $x$

Divide both sides of the equation by $0.041$: $x=\frac{262.40}{0.041}=6400$.

Answer:

$6400$