Interest problems Using Systems of Equations Interest Problems

Interest problems Using Systems of Equations

Interest Problems Ann invested $12, 000 in two bank accounts. One of the accounts pays 6% annual interest, and the other account pays 5% annual interest. If the combined interest earned in both accounts after a year was $700, how much money was invested in each account? Step 1 You must assign variables x = amount invested at 6% $12, 000 = total money invested in both accounts y = amount invested at 5% $700 = total interest earned in both accounts

Step 2 Equations must be properly set up! x + y = 12, 000. 06 x +. 05 y = 700

System of Equations

Making the Equations Nice x + y = 12, 000 -> x + y = 12, 000. 06 x +. 05 y = 700 -> 6 x + 5 y = 70, 000

Methods to Solve a System of Linear Equations 1)Graphing: paper, desmos, graphing calculator 2)Elimination 3)Substitution 4)Matrix Algebra

Step 3 Solve using Elimination Method x + y = 12, 000 -> times -6 -> -6 x – 6 y = -72000 6 x + 5 y = 70, 000 -> no change -> + 6 x + 5 y = 70, 000 -y = -2, 000 y = 2, 000 therefore x = 10, 000 Step 4 - Summarize $10, 000 was invested at 6% $2, 000 was invested at 5%

Substitution Method x + y = 12, 000 -> x = 12, 000 – y solve for either variable in first equation 6 x + 5 y = 70, 000 leave the other equation alone No substitute altered equation 1 into equation 2 6 ( 12, 000 – y ) + 5 y = 70, 000 72, 000 – 6 y + 5 y = 70, 000 72, 000 – y = 70, 000 - y = -2000 y = 2, 000 therefore x = 10, 000

Casey invested $20, 000 in two bank accounts. One of the accounts pays 8% annual interest, and the other account pays 7% annual interest. If the combined interest earned in both accounts after a year was $1, 525, how much money was invested in each account? Step 1 Assign Variables Step 2 Set up Equations Step 3 Solve Equations using elimination or substitution method (check with graphing method) Step 4 Summarize System of Equations ixl. com Algebra 1 skill U 1, U 2, U 8, U 10 to 50 Due Tuesday, August 28 by 5 PM When done continue with ixl sections A, B, C to 50