Last year Sarah invested money in two accounts. The first account had an interest rate of 3%3% and the second account had an interest rate of 4%4%. If she invested $700$700 more in the first account than the second and her total interest income was $553$553, how much did she invest at each rate?Step 1 of 3 : Complete the following table by entering the missing values. Enter the rates in decimal form.
Question
Last year Sarah invested money in two accounts. The first account had an interest rate of 3%3% and the second account had an interest rate of 4%4%. If she invested 700 more in the first account than the second and her total interest income was 553, how much did she invest at each rate?Step 1 of 3 : Complete the following table by entering the missing values. Enter the rates in decimal form.
Solution
First, let's convert the interest rates from percentages to decimals. 3% becomes 0.03 and 4% becomes 0.04.
Next, let's denote the amount Sarah invested in the second account as x. Therefore, the amount she invested in the first account is x + $700.
Sarah's total interest income was $553. This income came from both accounts, so we can set up the following equation:
0.03(x + 700) + 0.04x = 553
Now, we can solve this equation to find the value of x, which represents the amount Sarah invested in the second account. After finding x, we can easily find the amount she invested in the first account by adding $700 to x.
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