A set designer is hammering nails along the top edge of a wall with a length of 3x feet, where x is an integer, that will be used to hang garland. The designer hammers the first nail at the left edge of the wall. The designer then hammers an additional nail every 3/8 feet along the entire length of the wall, starting from the first nail and with the last nail being hammered at the right edge of the wall. Which equation best represents this situation, where y is the number of nails the designer hammers along the entire length of the wall?

A set designer is hammering nails along the top edge of a wall with a length of 3x feet... | SAT Linear equations in two variables Practice

A set designer is hammering nails along the top edge of a wall with a length of $3x$ feet, where $x$ is an integer, that will be used to hang garland. The designer hammers the first nail at the left edge of the wall. The designer then hammers an additional nail every $\dfrac{3}{8}$ feet along the entire length of the wall, starting from the first nail and with the last nail being hammered at the right edge of the wall. Which equation best represents this situation, where y is the number of nails the designer hammers along the entire length of the wall?

Answer: D. $y=8x+1$

Explanation:1. Define the variables and given information: Length of the wall $L = 3x$ feet. Distance between consecutive nails (interval length) $d = \dfrac{3}{8}$ feet. The first nail is at the beginning (left edge) of the wall. The last nail is at the end (right edge) of the wall. $y$ is the total number of nails.

Calculate the number of intervals: The nails divide the wall into a number of intervals of length $d$ . Number of intervals = $\dfrac{\text{Total length of wall}}{\text{Length of one interval}}$ Number of intervals = $\dfrac{L}{d} = \dfrac{3x \text{ feet}}{\dfrac{3}{8} \text{ feet/interval}}$ Number of intervals = $3x \times \dfrac{8}{3} = 8x$ intervals.
Calculate the total number of nails: If there are $N$ intervals, and there is a nail at the beginning of the first interval and at the end of each interval (including the last one), the total number of nails is $N+1$ . Here, the number of intervals is $8x$ . So, the total number of nails $y = (\text{Number of intervals}) + 1$ . $y = 8x + 1$ .
Compare with the given options: The equation $y = 8x + 1$ matches option [D].

Conclusion:Assuming the nail spacing is $\dfrac{3}{8}$ feet, the equation that best represents the situation is $y=8x+1$ .

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SAT Linear equations in two variables practice question

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