ANSWER
The amount invested at 5% interest is $2598.00
The amount invested at 10% interest is $13,046.00
Explanation:
Given parameters
• Let the amount invested at a 5% rate be x
,
• The total amount received = $1434.50
George invested $x at 5% interest
George also invested $56 more than 5 times that amount at 10%
This can be written mathematically as
56 + 5(x)
56 + 5x ----------- amount invested at 10% interest
The total amount received = amount invested at 5% * interest rate + amount invested at 10% * interest rate
Mathematically,
1434.50 = 0.05(x) + 0.10(56 + 5x)
The next thing is to open the parentheses
1434.50 = 0.05x + 0.1 * 56 + 0.1 * 5x
1434.50 = 0.05x + 5.6 + 0.5x
Collect the like terms
1434.50 = 0.05x + 0.5x + 5.6
1434.50 = 0.55x + 5.6
Substract 5.6 from both sides
1434.50 - 5.6 = 0.55x + 5.6 - 5.6
1428.9 = 0.55x
Divide both sides by 0.55
1428.9/0.55 = 0.55x/0.55
1428.9/0.55 = x
x = $2,598.00
Hence, the amount invested at 5% interest is $2598.00
The next thing is to find the amount invested at 10% can be calculated below
The amount invested at 10% interest is 56 + 5x
Where x = $2598.00
Amount invested at 10% interest = 56 + 5x
Amount invested at 10% interest = 56 + 5(2598.00)
Amount invested at 10% interest = 56 + 12990
Amount invested at 10% interest = $13,046.00
Hence, the amount invested at 10% interest is $13,046.00