a vendor has learned that, by pricing pretzels at $1.50 sales will reach 91 pretzels per day. raising the price to $2.25 will cause the sales to fall to 58 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that models the number of pretzels sold per day when the price is x dollars each

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sailuyarlas122076 sailuyarlas122076

02-08-2017
Mathematics

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a vendor has learned that, by pricing pretzels at $1.50 sales will reach 91 pretzels per day. raising the price to $2.25 will cause the sales to fall to 58 pretzels per day. Let y be the number of pretzels the vendor sells at x dollars each. Write a linear equation that models the number of pretzels sold per day when the price is x dollars each

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Yna9141 Yna9141 · Answer 1 · 2017-08-11T15:11:19+02:00

The givens can be expressed as the abscissa and ordinate of two points. The first point is (1.5, 91). The second point would then have the coordinates of (2.25, 58)
We are given with two points so we can derive the equation using the two-point form.
That is,
y – y1 = ((y2 – y1)/(x2 – x1))(x – x1)

We may choose which among our derived coordinates will be 1 and 2. Substituting to the equation,
y – 91 = ((58 – 91)/(2.25 – 1.5))(x – 1.5)
y – 91 = -44(x – 1.5)
Simplifying further,
y – 91 = -44x + 66

y = -44x + 157

Thus, the equation above gives the number of pretzels that can be sold given the price.