# Two investments totaling $53,500 produce an annual income of $4,030. One investment yields 10%...

## Question:

Two investments totaling $53,500 produce an annual income of $4,030. One investment yields 10% per year, while the other yields 4% per year.

How much is invested at each rate?

## Basic Algebra - Rate of Return:

This problem calls for the use of algebra, a branch of mathematics that dates back centuries. Algebraic equations substitute letters for numbers. In doing so, they enable users to express real-world variables and relationships into equations and solve for unknowns.

## Answer and Explanation:

We are given the following two equations:

.10x + .04y = $4,030

x + y = $53,500

By embedding the second equation into the first, we can solve the problem. The computations and results are outlined below.

.10($53,500 - y) + .04y = $4,030

$5,350 - .10y + .04y = $4,030

-.06y = -$1,320

y = $22,000

We know y. Now, we can plug y into the second equation to solve x. See below.

x + $22,000 = $53,500

x = $31,500

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#### Learn more about this topic:

from SAT Subject Test Mathematics Level 2: Tutoring Solution

Chapter 4 / Lesson 10