Winston has just received his monthly credit card statement. He placed 7 charges on his card in the last month with a mean of \( \$ 21.09 \) per charge. He knows that 6 of the charges were as follows: Determine the amount of the \( 7^{\text {th }} \) charge. \( \$ 21.49, \$ 22.40, \$ 17.40, \$ 21.76, \$ 15.86, \$ 16.40 \) Copy Data

To find the amount of the 7th charge, we can use the mean of the 6 known charges and the total sum of all 7 charges. Given: - Mean of 6 charges = $21.09 - Charges: $21.49, $22.40, $17.40, $21.76, $15.86, $16.40 Let's denote the 7th charge as \( x \). The sum of all 7 charges is equal to the mean multiplied by the total number of charges: \[ \text{Sum of all 7 charges} = \text{Mean} \times \text{Total number of charges} \] Substitute the given values: \[ 21.09 \times 7 = 21.49 + 22.40 + 17.40 + 21.76 + 15.86 + 16.40 + x \] Now, we can solve for \( x \) to find the amount of the 7th charge. Solve the equation by following steps: - step0: Solve for \(x\): \(21.09\times 7=21.49+22.4+17.4+21.76+15.86+16.4+x\) - step1: Multiply the numbers: \(147.63=115.31+x\) - step2: Swap the sides: \(115.31+x=147.63\) - step3: Move the constant to the right side: \(x=147.63-115.31\) - step4: Subtract the numbers: \(x=32.32\) The amount of the 7th charge is $32.32.