A community garden charges a one-time registration fee plus a monthly fee to plot and main… — SAT

A community garden charges a one-time registration fee plus a monthly fee to plot and maintain a garden bed. The total cost, $y$ , in dollars, of maintaining a garden bed for $x$ months is given by the equation $y = 15x + 45$ . If a gardener spent a total of $165$ dollars, for how many months did they maintain the garden bed?

Answer: 8 months

Answer

The correct answer is 8. Setting the total cost y equal to 165 in the linear equation yields 165 = 15x + 45. Subtracting 45 from both sides gives 120 = 15x, and dividing by 15 results in x = 8 months.

To find the number of months the gardener maintained the garden bed, substitute the total spent,

165

, for

y

in the equation

y = 15x + 45

. This results in

165 = 15x + 45

. Subtracting

45

from both sides of the equation yields

120 = 15x

. Dividing both sides by

15

gives

x = 8

. Thus, the garden bed was maintained for 8 months.

Step-by-Step Solution

Substitute 165 for y in the equation.

165 = 15x + 45

The variable y represents the total cost in dollars, which is given as 165.

Subtract 45 from both sides of the equation.

120 = 15x

This isolates the variable term by subtracting the constant registration fee.

Divide both sides of the equation by 15.

x = 8

This solves for x, the number of months.

Key Concept

Solving for a variable in a linear equation representing a real-world scenario.

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