Page 157

hendricks_beginning_algebra_1e_ch1_3

Section 2.6 Percent, Rate, and Mixture Problems 155 �� ������������������������ �������������������� Use the simple interest formula to solve each problem. 2a. Marcus invested $10,000 in two accounts. He invested $2000 in a savings account that pays 3.5% annual interest and the remaining amount in a CD that pays 6% annual interest. How much interest did he earn from the two accounts in one year? Solution 2a. What is unknown? The total interest earned from the two accounts is unknown. What is known? A total of $10,000 was invested, $2000 invested at 3.5% and $8000 invested at 6%. Account Principal × Rate × Time = Interest Savings 2000 3.5% = 0.035 1 yr (2000) (0.035) (1) = 70 CD 10,000 - 2000 = 8000 6% = 0.06 1 yr (8000) (0.06) (1) = 480 The total interest earned from the two accounts is given by Total interest = (2000)(0.035)(1) + (8000)(0.06)(1) = 70 + 480 = 550 So, Marcus earned a total of $550 in interest from the two accounts. 2b. Rosa has $5000 to invest. She invests part of her money in a savings account that earns 3% annual interest and the rest in a CD that pays 5% annual interest. If the total interest earned in 1 yr is $230, how much did she invest in each account? Solution 2b. What is unknown? The amount invested in each of the accounts is unknown. Let x = amount invested in the savings account. Then 5000 - x = amount invested in the CD. What is known? The total invested is $5000 and the total interest earned from the two accounts is $230. Account Principal × Rate × Time = Interest Savings x 3% = 0.03 1 yr (x)(0.03)(1) or 0.03x CD 5000 - x 5% = 0.05 1 yr (5000 - x)(0.05)(1) or 0.05(5000 - x) Total $5000 $230 The sum of the interest from the savings account and the interest from the CD account is the total interest earned. 0.03x + 0.05(5000 - x) = 230 0.03x + 250 - 0.05x = 230 -0.02x + 250 = 230 -0.02x + 250 - 250 = 230 - 250 -0.02x = -20 -0.02x -0.02 = -20 -0.02 Express the relationship. Apply the distributive property. Combine like terms. Subtract 250 from each side. Simplify. Divide each side by -0.02. x = 1000 Simplify. So, Rosa invested $1000 in the 3% account and $5000 - $1000 = $4000 in the 5% account.


hendricks_beginning_algebra_1e_ch1_3
To see the actual publication please follow the link above