You invest in: Bonds yielding an interest rate of 1.6 percent, Utility Stock yielding an interest rate of 5.2 percent, and a Bank Certificate yielding an interest rate of 7.5 percent. The total interest earned in all three accounts in one year was \( \$ 4,373.00 \) dollars. The amount allocated to the bonds was 500 less than the amount allocated to the bank certificate. The amount allocated to the utility stock was 4 times the amount allocated to the bonds. What was the total amount of money the person had to invest? The total amount invested was \( \$ \)

Let's denote the amount allocated to the bonds as \( x \) dollars. Given: - The amount allocated to the utility stock is 4 times the amount allocated to the bonds, so it is \( 4x \) dollars. - The amount allocated to the bank certificate is 500 more than the amount allocated to the bonds, so it is \( x + 500 \) dollars. The total interest earned in one year from all three accounts is $4,373.00. The interest earned from each investment is calculated as follows: - Interest from bonds: \( 0.016x \) dollars - Interest from utility stock: \( 0.052 \times 4x = 0.208x \) dollars - Interest from bank certificate: \( 0.075 \times (x + 500) \) dollars The total interest earned is the sum of the interests from all three investments: \[ 0.016x + 0.208x + 0.075(x + 500) = 4373 \] Now, we can solve this equation to find the value of \( x \), which represents the amount allocated to the bonds. Once we have the value of \( x \), we can calculate the total amount invested by adding the amounts allocated to the bonds, utility stock, and bank certificate. Solve the equation by following steps: - step0: Solve for \(x\): \(0.016x+0.208x+0.075\left(x+500\right)=4373\) - step1: Add the terms: \(0.224x+0.075\left(x+500\right)=4373\) - step2: Move the expression to the left side: \(0.224x+0.075\left(x+500\right)-4373=0\) - step3: Calculate: \(0.299x-4335.5=0\) - step4: Move the constant to the right side: \(0.299x=0+4335.5\) - step5: Remove 0: \(0.299x=4335.5\) - step6: Divide both sides: \(\frac{0.299x}{0.299}=\frac{4335.5}{0.299}\) - step7: Divide the numbers: \(x=14500\) The amount allocated to the bonds is $14,500. Now, we can calculate the total amount invested by adding the amounts allocated to the bonds, utility stock, and bank certificate: - Bonds: $14,500 - Utility Stock: $4 \times 14,500 = $58,000 - Bank Certificate: $14,500 + $500 = $15,000 Total amount invested = $14,500 + $58,000 + $15,000 = $87,500 Therefore, the total amount of money the person had to invest was $87,500.