Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. A rental car company is running two specials. Customers can pay $47 to rent a compact car for the first day plus $5 for each additional day, or they can rent the same car for $48 the first day and $4 for every additional day beyond that. Christina notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How many additional days does Christina want? How much would Christina pay in total? For _____ additional days, Christina would pay $_____ either way.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  A rental car company is running two specials. Customers can pay $47 to rent a compact car for the first day plus $5 for each additional day, or they can rent the same car for $48 the first day and $4 for every additional day beyond that. Christina notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How many additional days does Christina want? How much would Christina pay in total?   For _____ additional days, Christina would pay $_____ either way.

Bytelearn · Accepted Answer

Define Equations:  Step 1: Define the equations for the two rental specials. For the first special, the total cost $ C_1 $ is $47 for the first day plus $5 for each additional day $ x $: $$ C_1 = 47 + 5x $$ For the second special, the total cost $ C_2 $ is $48 for the first day plus $4 for each additional day $ x $: $$ C_2 = 48 + 4x $$Set Equations Equal:  Step 2: Set the equations equal to find when the costs are the same. $$ 47 + 5x = 48 + 4x $$ Subtract 47 from both sides: $$ 5x = 1 + 4x $$ Subtract 4x from both sides: $$ x = 1 $$Calculate Total Cost:  Step 3: Calculate the total cost for 1 additional day using either equation. Using $ C_1 $: $$ C_1 = 47 + 5(1) $$ $$ C_1 = 47 + 5 $$ $$ C_1 = 52 $$

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