An investor received $1400 interest per annum from a sum of money, with part of it invested at 10% and the remainder at 7% simple interest. This investor found that if she interchanged the amounts she had invested she could increase her return by $90p annum. Calculate the total ampunt invested.

Question

An investor received  $1400 interest per annum from a sum of money, with part of it invested at  10% and the remainder at  7% simple interest. This investor found that if she interchanged the amounts she had invested she could increase her return by  $90p annum. Calculate the total ampunt invested.

Bytelearn · Accepted Answer

Denote Investments: Let's denote the amount invested at 10% as x and the amount invested at 7% as y. The total interest from these investments is $1400 per annum. We can write the first equation for the interest received from both investments: 0.10x + 0.07y = 1400Write Equations: If the investor interchanges the amounts, the amount invested at 10% becomes y and the amount invested at 7% becomes x. The new total interest received is $1400 + $90 = $1490 per annum. We can write the second equation for the interest received after interchanging the amounts: 0.10y + 0.07x = 1490Solve System: Now we have a system of two equations with two variables: 1) 0.10x + 0.07y = 1400 2) 0.07x + 0.10y = 1490 We can solve this system using the method of substitution or elimination. Let's use the elimination method by multiplying the first equation by 10 and the second equation by 7 to eliminate y: 10*(0.10x + 0.07y) = 10*1400 7*(0.07x + 0.10y) = 7*1490Eliminate Variables: After multiplying we get: 1) 1x + 0.7y = 14000 2) 0.49x + 0.7y = 10430 Now we can subtract the second equation from the first to eliminate y: (1x - 0.49x) + (0.7y - 0.7y) = 14000 - 10430Calculate Values: Simplifying the subtraction gives us: 0.51x = 3570 Now we can solve for x by dividing both sides by 0.51: x = 3570 / 0.51Substitute x: Calculating the value of x gives us: x = 7000 This is the amount invested at 10%. Now we can use this value to find y by substituting x into one of the original equations.Solve for y: Substituting x into the first equation: 0.10*7000 + 0.07y = 1400 700 + 0.07y = 1400 Now we can solve for y by subtracting 700 from both sides: 0.07y = 1400 - 700Find Total Amount: Simplifying the subtraction gives us: 0.07y = 700 Now we can solve for y by dividing both sides by 0.07: y = 700 / 0.07Calculating the value of y gives us: y = 10000 This is the amount invested at 7%. Now we can find the total amount invested by adding x and y.The total amount invested is: x + y = 7000 + 10000Calculating the total gives us: Total amount invested = 17000 This is the final answer to the question prompt.

Full solution

More problems from Multi-step problems with percents

Related topics