Questions: Let x be the amount of 90-octane gas used in the mixture. Complete the following chart. Type of Gas Quantity % Isooctane Amount of Isod 90-octane x 90% 99-octane 400 99% Mixture x+400 94% (Simplify your answers. Use integers or decimals for any numbers in the expression.)

Solution Steps

To complete the chart, we need to calculate the amount of isooctane in each type of gas and the mixture. The amount of isooctane is given by the product of the quantity and the percentage of isooctane.

1. For the 90-octane gas, the amount of isooctane is \(0.90 \times x\).
2. For the 99-octane gas, the amount of isooctane is \(0.99 \times 400\).
3. For the mixture, the total amount of isooctane should be equal to the sum of the isooctane from both types of gas, and it should also be equal to \(0.94 \times (x + 400)\).

The amount of isooctane in the 90-octane gas is given by: \[ \text{Amount of isooctane in 90-octane gas} = 0.90 \times x \] Since \( x = 0 \) in the given output, the amount of isooctane in the 90-octane gas is: \[ 0.90 \times 0 = 0.0 \]

The amount of isooctane in the 99-octane gas is given by: \[ \text{Amount of isooctane in 99-octane gas} = 0.99 \times 400 \] Calculating this, we get: \[ 0.99 \times 400 = 396.0 \]

The total amount of isooctane in the mixture is the sum of the isooctane from both types of gas: \[ \text{Total amount of isooctane in the mixture} = 0.0 + 396.0 = 396.0 \]

The required amount of isooctane in the mixture is given by: \[ \text{Required amount of isooctane in the mixture} = 0.94 \times (x + 400) \] Since \( x = 0 \), we have: \[ 0.94 \times (0 + 400) = 0.94 \times 400 = 376.0 \]

Final Answer