Set up an algebraic equation and then solve. Jim invested an...

Set up an algebraic equation and then solve. Jim invested an inheritance in two separate banks. One bank offered $5.5 \%$ annual interest rate and the other $61 / \% .$ He invested twice as much in the higher yielding bank account than he did in the other. If his total simple interest for 1 year was $\$ 4,860,$ then what was the amount of his inheritance?

Set up an algebraic equation and then solve.
Jim invested an inheritance in two separate banks. One bank offered $5.5 \%$ annual interest rate and the other $61 / \% .$ He invested twice as much in the higher yielding bank account than he did in the other. If his total simple interest for 1 year was $\$ 4,860,$ then what was the amount of his inheritance?

Key Concepts

Solving Linear Equations

Once the algebraic equation is set up, the next step is to solve for the unknown variable(s). This involves using algebraic operations such as addition, subtraction, multiplication, division, and sometimes substitution to isolate and determine the value of the variables. Mastery of this technique is essential for resolving the problem and finding the correct numerical answers.

Simple Interest

This concept involves calculating interest earned over a period based on the principal amount, rate, and time. The simple interest formula is I = P × r × t, where I represents the interest, P stands for the principal, r is the rate (expressed as a decimal), and t is the time. Understanding this formula is crucial when dealing with problems that involve constant percentage yields over time.

Conversion of Percentage to Decimal

When working with interest rates or any percentages in algebraic problems, it's necessary to convert percentages to decimals. This is done by dividing the percentage value by 100. For example, an interest rate of 5.5% becomes 0.055 in decimal form. This step is essential for accurate representation and manipulation of the rate in algebraic equations.

Algebraic Equation Setup

This key concept involves translating a word problem into an algebraic equation by defining variables and expressing relationships algebraically. In investment problems, this typically means assigning variables to the unknown principal amounts and using the given conditions – such as ratios or total interest – to set up one or more equations that model the situation.

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