Question

gabriel sells televisions. he earns a fixed amount for each television and an additional $30 if the buyer gets an extended warranty. if gabriel sells 14 televisions with extended warranties, he earns $1,120. how much is the fixed amount gabriel earns for each television? the fixed amount gabriel earns for each television he sells is $

Explanation:

Step1: Define variables

Let \( x \) be the fixed amount (in dollars) Ci earns for each television sold, and \( y = 30 \) be the additional amount for extended warranty. Let \( n = 14 \) be the number of televisions with extended warranty, and \( T = 1120 \) be the total earnings.

Step2: Set up the equation

The total earnings come from the fixed amount per television and the additional amount for extended warranty. So the equation is:

$$ n(x + y) = T $$

Substitute the known values: \( n = 14 \), \( y = 30 \), \( T = 1120 \)

$$ 14(x + 30) = 1120 $$

Step3: Solve for \( x \)

First, divide both sides by 14:

$$ x + 30=\frac{1120}{14} $$

$$ x + 30 = 80 $$

Then, subtract 30 from both sides:

$$ x=80 - 30 $$

$$ x = 50 $$

Answer:

50