Javier often orders party trays from his favorite Mexican food restaurant for company events. For a recent company event, he spent $259 on 4 burrito platters and 2 taco platters. For a company meeting, he spent $284 on 4 burrito platters and 4 taco platters. How much does each type of platter cost? and

Jeff is a shoe salesman, and he works on commission. This week, there is a special incentive to sell shoes and boots by a certain company. Yesterday, Jeff sold 8 pairs of shoes and 7 pairs of boots, earning $188 in commission. Today, he sold 8 pairs of shoes and 6 pairs of boots, earning a total commission of $168. How much does Jeff earn for the sale of each type of footwear?

1. 1 Burrito Platter = $58.50 , 1 Taco platter = $12.50

2. One pair of boots = $20 , One pair of shoes = $6

Step-by-step explanation:

1. Let the cost of one burrito platter be x and one taco platter be y.

4x + 2y = 259 --- Equation 1

4x + 4y = 284 --- Equation 2

Equations 2-1: 4x + 4y - 4x - 2y = 284 - 259

2y = 25

y = 25 ÷ 2

y = 12.50 (Taco platter)

Substitute y = 12.50 into Equation 1:

4x + 2y = 259

4x + 2(12.50) = 259

4x + 25 = 259

4x = 259 - 25

    = 234

x = 234 ÷ 4

x = 58.50 (Burrito platter)

2. Let the cost of one pair of boots be x and one pair of shoes be y.

7x + 8y = 188 --- Equation 1

6x + 8y = 168 --- Equation 2

Equations 1-2: 7x + 8y - 6x - 8y = 188 - 168

x = 20 (Boots)

Substitute x = 20 into Equation 2:

6x + 8y = 168

6(20) + 8y = 168

120 + 8y = 168

8y = 168 - 120

    = 48

y = 48 ÷ 8

y = 6 (Shoes)

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation: