Solve each problem. See Example 4. Cody sells some property for \$240,000. The money will be paid off in two ways: a short-term note at 2% interest and a long-term note at 2.5%. Find the amount of each note if the total annual interest paid is \$5500.

Verified step by step guidance

Define variables for the amounts of the two notes. Let $x$ be the amount of the short-term note at 2% interest, and $y$ be the amount of the long-term note at 2.5% interest.

Write an equation representing the total amount of the property sold: $x + y = 240000$.

Write an equation representing the total annual interest paid. The interest from the short-term note is \$0.02x$ and from the long-term note is \$0.025y$. The total interest is $5500$, so the equation is $0.02x + 0.025y = 5500$.

Use the first equation to express one variable in terms of the other, for example, $y = 240000 - x$.

Substitute this expression for $y$ into the interest equation and solve for $x$. Once $x$ is found, substitute back to find $y$.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Simple Interest Formula

Simple interest is calculated using the formula I = P × r × t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years. Understanding this formula is essential to relate the interest earned from each note to its principal and rate.

System of Linear Equations

A system of linear equations involves two or more equations with multiple variables. Solving such systems helps find unknown values—in this case, the amounts of the short-term and long-term notes—by using methods like substitution or elimination.

Total Amount Constraint

The total amount of the property sold ($240,000) is split between two notes. This constraint forms one equation where the sum of the two note amounts equals the total sale price, providing a key relationship to solve the problem.

Recommended video: