Sheryl won 60,000 on a slot machine in Las Vegas. She...

Sheryl won 60,000 on a slot machine in Las Vegas. She invested part of the money at $2 \%$ simple interest and the rest at $3 \%$. In one year, she earned a total of 1600 in interest. How much was invested at each rate?

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Key Concepts

Mixture Problems

A type of problem that involves combining different components in varying proportions to meet a certain total or achieve a specific characteristic. It often requires setting up equations that balance the sums and rates of the mixed components.

Percentage to Decimal Conversion

Converting percentages to decimals is essential for calculations involving rates, such as interest rates. This conversion facilitates the computation by allowing percentages to be expressed as fractions of one instead of whole numbers.

Simple Interest

A method of calculating interest whereby the interest charge is determined solely by the original principal, the interest rate, and the time period, without the effects of compounding. This concept is fundamental when determining earnings from different investment amounts over a set period.

System of Linear Equations

A mathematical approach involving multiple equations with unknown variables that can be solved simultaneously. It is especially useful in problems where a total amount is partitioned in different ways based on varying conditions or rates.

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