1 A pizza parlor charges 1 for each

1. ) A pizza parlor charges $1 for each vegetable topping and $2 for each meat topping. You want at least five toppings on your pizza. You have $10 to spend on toppings. How many of each type of topping can you get on your pizza? Algebra 3 Section 3. 3 Systems of Inequalities 1(vegetable topping) + 2(meat topping) ≤ 10 {value of topping times number of toppings equals total} number of toppings ≥ 5 {at least 5 toppings} x = number of vegetable toppings y = number of meat toppings x + 2 y ≤ 10 {1 st statement as an inequality} x + y ≥ 5 {2 nd statement as an inequality} Graph the system. The overlapping coordinates, which fit the situation, is the solution x+y≥ 5 -x y is meat ($2) 5 meat 4 meat 3 meat 2 meat 1 meat 0 meat -x y ≥ -x + 5 {subtracted x from each side} x is vegetable ($1) 0 vegetable 1 or 2 vegetable 2, 3, or 4 vegetable 3, 4, 5, or 6 vegetable 4, 5, 6, 7, or 8 vegetable 5, 6, 7, 8, 9, or 10 vegetable © Mr. Sims

You want to decorate a party hall with a total of at least 40 red and yellow balloons, with a minimum of 25 yellow balloons. Write and graph a system of inequalities to model the situation. r = red balloons y = yellow balloons r + y ≥ 40 y ≥ 25 {at least 40 red and yellow balloons} {minimum of 25 yellow balloons} r + y ≥ 40 -r -r y ≥ -r + 40 {subtracted r from each side} y ≥ 25 Since the number of balloons must be a whole number, only the points in the overlap that represent whole numbers are solutions of the problem. For example: (0, 40) , (0, 41) , (1, 39) , (1, 40) , (2, 38) , etc. © Mr. Sims

Review of graphing absolute value inequalities Graph y ≤ 3|x – 1| – 2 The boundary is the graph of y = 3|x – 1| – 2 in standard form, y = a|x – h| + k, (h , k) is the vertex a is the slope of the right branch vertex = (1 , -2) slope of right branch = 3 use a solid line because of the “≤” sign shade down the y-axis because of the ≤ sign © Mr. Sims

Solve the system by graphing. absolute value inequality in standard form, y = a|x – h| + k, (h , k) is the vertex a is the slope of the right branch vertex = slope of right branch = 2 the overlap is the solution © Mr. Sims

Notice the ≥ and ≤ signs, meaning solid lines For y ≤ |3 x|, in standard form, it is y ≤ 3|x| vertex is at (0, 0) absolute value inequality in standard form, y = a|x – h| + k, (h , k) is the vertex a is the slope of the right branch © Mr. Sims

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