Question

type the correct answer in each box. use numerals instead of words.
oscar is buying 4 new tires for his car. he has $240 budgeted for the tires, but can afford to pay $35 more or less than that amount. this equation represents the situation:
|4t - 240| = 35.
use this information to complete this statement.
to keep within his budget, oscar can pay a minimum of $ \underline{\quad} and a maximum of $ \underline{\quad} for each tire.

Explanation:

Step1: Solve the absolute - value equation

The absolute - value equation is \(|4t - 240|=35\). By the definition of absolute value, if \(|x| = a\) (\(a\geq0\)), then \(x=a\) or \(x = - a\). So we have two cases:
Case 1: \(4t-240 = 35\)
Add 240 to both sides of the equation: \(4t=35 + 240\)
\(4t=275\)
Divide both sides by 4: \(t=\frac{275}{4}=68.75\)
Case 2: \(4t - 240=-35\)
Add 240 to both sides of the equation: \(4t=-35 + 240\)
\(4t = 205\)
Divide both sides by 4: \(t=\frac{205}{4}=51.25\)

Step2: Determine the minimum and maximum values

The value of \(t\) represents the cost of each tire. From the two solutions of the equation, the smaller value of \(t\) is the minimum cost per tire and the larger value of \(t\) is the maximum cost per tire.

Answer:

To keep within his budget, Oscar can pay a minimum of \(\$51.25\) and a maximum of \(\$68.75\) for each tire.