Modeling with Systems of Linear Inequalities

Kyle asks his friend Jane to guess his age and his grandmother's age. Kyle says his grandmother is not more than 80 years old. He says his grandmother's age is, at most, 3 years less than 3 times his own age. Jane writes this system of inequalities to represent k, Kyle's age, and g, Kyle's grandmother's age. Inequality 1: g > 80 Inequality 2: g ≤ 3k - 3 Which inequality did Jane write incorrectly, and how could it be corrected?

A.) Inequality 1 is incorrect; it should be g ≤ 80.

A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?

A.) The pool is 1 meter deep.

Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?

A.) l ≤ 12 2l + 2w < 30

A school is planning for an addition in some open space next to the current building. The existing building ends at the origin. The graph represents the system of equations that can be used to define the space for the addition. What is the system of equations that matches the graph?

A.) y ≤ 3x y > -2x - 1

Irina wants to build a fence around a rectangular vegetable garden so that it has a width of at least 10 feet. She can use a maximum of 150 feet of fencing. The system of inequalities that models the possible lengths, l, and widths, w, of her garden is shown. w ≥ 10 2l + 2w ≤ 150 On a coordinate plane, 2 solid straight lines are shown. The first line is horizontal to the y-axis at y = 10. Everything above the line is shaded. The second line has a negative slope and goes through (0, 75) and (75, 0). Everything to the left of the line is shaded. Which length and width are possible dimensions for the garden?

B.) l = 20 ft; w = 10 ft

Consider the system of inequalities and its graph. y ≥ x/4 y ≤ x - 3 In which section of the graph does the actual solution to the system lie?

C.) 3

y ≤ -0.75x y ≤ 3x - 2 In which section of the graph does the actual solution to the system lie?

D.) 4

A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

D.) t ≤ 40 8p + t ≤ 184