A car-rental company charges a flat fee of \0.40 per mile. For each mile beyond 150, the company charges \35 flat fee). After the airport surcharge is applied, a local tax of 8% is applied to the entire amount (including the \yxx>150$?

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Super-Hard SAT Math Question 3 | Free SAT Prep | Aniko

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Question 3·200 Super-Hard SAT Math Questions·Algebra

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A car-rental company charges a flat fee of $35 for a one-day rental. This fee includes up to 100 miles driven. For miles 101 through 150, the company charges $0.40 per mile. For each mile beyond 150, the company charges $0.60 per mile. An airport surcharge of 10% is applied only to the per-mile charges (not to the $35 flat fee). After the airport surcharge is applied, a local tax of 8% is applied to the entire amount (including the $35 flat fee and any surcharges).

Which equation gives the total cost $y$ , in dollars, for driving $x$ miles, where $x>150$ ?

For tiered linear cost questions, build the variable part in fixed chunks (here, $50$ miles plus $x-150$ miles). Then apply percent multipliers only to the parts they apply to (surcharge vs. tax), in the order described, and simplify to a single linear form $y=mx+b$ .

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Start with the $x>150$ per-mile subtotal

For $x>150$ , the per-mile subtotal is $0.40(50)+0.60(x-150)$ .

Be careful about what each percent applies to

The 10% airport surcharge multiplies only the per-mile subtotal. The 8% local tax is applied after that to the entire total (including the flat fee).

Multiply in the correct order

A safe order is: (1) per-mile subtotal, (2) multiply by $1.10$ , (3) add 35, (4) multiply the whole thing by $1.08$ .

Desmos Guide

Pick a test value with $x>150$

Choose a convenient value such as $x=200$ .

Compute the total directly from the rules

For $x=200$ :

Per-mile subtotal: $0.40(50)+0.60(200-150)$
Apply airport surcharge: multiply that per-mile subtotal by $1.10$
Add the $35 flat fee
Apply local tax: multiply the entire result by $1.08$

Check which equation matches

Enter each answer choice as a function in Desmos and make a table at $x=200$ . The correct equation is the one whose table value matches your computed total.

Step-by-step Explanation

Write the per-mile subtotal for $x>150$

If $x>150$ , then the per-mile miles are split as:

Miles 101–150: $50$ miles at $0.40
Miles beyond 150: $x-150$ miles at $0.60

So the per-mile subtotal is

0.40(50)+0.60(x-150).

Simplify the per-mile subtotal

\begin{aligned} 0.40(50)+0.60(x-150) &=20+0.60x-90\\ &=0.60x-70. \end{aligned}

Apply the 10% airport surcharge to per-mile charges only

A 10% surcharge multiplies the per-mile subtotal by $1.10$ :

1.10(0.60x-70)=0.66x-77.

Add the flat fee, then apply the 8% local tax to the entire amount

Add the $35 flat fee (not surcharged):

35+(0.66x-77)=0.66x-42.

Now apply the 8% tax (multiply by $1.08$ ):

y=1.08(0.66x-42).

Convert to fractions and state the equation

Write the multipliers as fractions: $1.08=\frac{27}{25}$ and $0.66=\frac{33}{50}$ .

\begin{aligned} y&=\frac{27}{25}\left(\frac{33}{50}x-42\right)\\ &=\frac{891}{1250}x-\frac{1134}{25}. \end{aligned}

Therefore, the equation is $y=\frac{891}{1250}x-\frac{1134}{25}$ .

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Step-by-step Explanation

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Step-by-step Explanation