Modeling with Two-Variable Linear Inequalities — Quiz

Question 1 • Mathematics I

Lola bought x pencils that cost 0 point 25 each and y erasers that cost 0 point 50 dollars She spent less than 3 dollars Which graph represents Lola’s purchase?

Answer

Image with description A graph titled "Lola's Purchase" shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 5. A dashed straight line has a negative slope and goes through 0 comma 3 and 12 comma 0. Everything to the left of the line is shaded.

Image with description A graph titled "Lola's Purchase" shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 10. A dashed straight line has a negative slope and goes through 0 comma 6 and 12 comma 0. Everything to the left of the line is shaded.

Image with description A graph titled "Lola's Purchase" shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 10. A solid straight line has a negative slope and goes through 0 comma 6 and 12 comma 0. Everything to the left of the line is shaded.

Image with description A graph titled "Lola's Purchase" shows number of pencils on the x-axis, from 0 to 20, and number of erasers on the y-axis, from 0 to 5. A solid straight line has a negative slope and goes through 0 comma 3 and 12 comma 0. Everything to the left of the line is shaded.

Explanation

The total cost is 0.25x + 0.50y, and Lola spent less than $3, so 0.25x + 0.50y < 3. If she buys no erasers, she can buy 3 ÷ 0.25 = 12 pencils; if she buys no pencils, she can buy 3 ÷ 0.50 = 6 erasers. Because the inequality is strict, the boundary is dashed. Choice B shows a dashed line through (12, 0) and (0, 6), with the affordable region shaded.

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