Jack invests $1000 at a certain annual interest rate, and he invests another $2000 at an annual rate that is one-half percent higher. If he receives a total of $160 interest in 1 year, at what rate is the $1000 invested?
+23245 Since 1 percent is 0.01, one-half percent is 0.005.
Let x be the interest rate of the $1000 investment; then x + 0.005 will be the interest rate of the $2000 investment.
Formula: (Amount Invested)(Interest Rate) + (Amount Invested)(Interest Rate) = (Interest Earned)
(1000)(x) + (2000)(x+0.005) = 160
1000x + 2000x + 10 = 160
3000x + 10 = 160
3000x = 150
x = 150 / 3000
x = 0.05 ---> The $1000 is invested at 5%.
Check: ($1000)(0.05) + ($2000)(0.055) = $50 + $110 = $160
+23245 Since 1 percent is 0.01, one-half percent is 0.005.
Let x be the interest rate of the $1000 investment; then x + 0.005 will be the interest rate of the $2000 investment.
Formula: (Amount Invested)(Interest Rate) + (Amount Invested)(Interest Rate) = (Interest Earned)
(1000)(x) + (2000)(x+0.005) = 160
1000x + 2000x + 10 = 160
3000x + 10 = 160
3000x = 150
x = 150 / 3000
x = 0.05 ---> The $1000 is invested at 5%.
Check: ($1000)(0.05) + ($2000)(0.055) = $50 + $110 = $160
