Interest problems Using Systems of Equations

Interest Problems Ann invested $12,000 in two bank accounts 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 .06x + .05y = 700

System of Equations

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

Methods to Solve a System of Linear Equations Graphing: paper, desmos, graphing calculator Elimination Substitution Matrix Algebra

Step 3 Solve using Elimination Method x + y = 12,000 -> times -6 -> -6x – 6y = -72000 6x + 5y = 70,000 -> no change -> + 6x + 5y = 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 6x + 5y = 70,000 leave the other equation alone No substitute altered equation 1 into equation 2 6 ( 12,000 – y ) + 5y = 70,000 72,000 – 6y + 5y = 70,000 72,000 – y = 70,000 - y = -2000 y = 2,000 therefore x = 10,000

System of Equations ixl.com Algebra 1 skill U1,U2,U8,U10 to 50 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 U1,U2,U8,U10 to 50 Due Tuesday, August 28 by 5 PM When done continue with ixl sections A, B, C to 50