One travel association claims that each US household saves an average of $\$ 1148$ in taxes because of the tax revenue generated by leisure and business travel. Suppose there is a ratio of $\$ 9: \$ 19$ between tax revenue generated by business travel and by leisure travel. How many dollars would the average US household save in taxes because of the tax revenue generated by business travel?

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Q. One travel association claims that each US household saves an average of

\$ 1148

in taxes because of the tax revenue generated by leisure and business travel. Suppose there is a ratio of

\$ 9: \$ 19

between tax revenue generated by business travel and by leisure travel. How many dollars would the average US household save in taxes because of the tax revenue generated by business travel?

Define Total Tax Savings: Let's denote the total tax savings from both business and leisure travel as $T$ , which is given as $1148$ . The ratio of tax revenue generated by business travel to leisure travel is $9:19$ . We can represent the amount saved from business travel as $9x$ and from leisure travel as $19x$ , where $x$ is a common factor representing the amount saved per unit ratio. The sum of these two amounts should equal the total tax savings, $T$ .
Write Equation with Ratios: We can write the equation based on the given ratio and total tax savings: $9x + 19x = T$ . We know that $T = 1148$ , so we can substitute this value into the equation to find $x$ .
Solve for x: The equation becomes $9x + 19x = 1148$ . Combining like terms, we get $28x = 1148$ .
Calculate Value of x: To find the value of $x$ , we divide both sides of the equation by $28$ : $x = \frac{1148}{28}$ .
Find Business Travel Savings: Calculating the value of $x$ , we get $x = 41$ . This means that for every unit in the ratio, the average US household saves $41$ in taxes.
Find Business Travel Savings: Calculating the value of $x$ , we get $x = 41$ . This means that for every unit in the ratio, the average US household saves $41$ in taxes.Now, we need to find out how much of the $1148$ is due to business travel. Since the ratio for business travel is $9x$ , we multiply $9$ by the value of $x$ we just found: $9 \times 41$ .
Find Business Travel Savings: Calculating the value of $x$ , we get $x = 41$ . This means that for every unit in the ratio, the average US household saves $41$ in taxes.Now, we need to find out how much of the $1148$ is due to business travel. Since the ratio for business travel is $9x$ , we multiply $9$ by the value of $x$ we just found: $9 \times 41$ .Calculating the amount saved from business travel, we get $9 \times 41 = 369$ .