Understanding and solving linear equations in three variables

Find the amounts of 20% salt solution and 8% salt solution that should be mixed together to make 500 ml of 15% salt solution.

• 291.67 ml of 20% salt solution,
  208.33 ml of 8% salt solution

• 280 ml of 20% salt solution,
  220 ml of 8% salt solution

• 208.33 ml of 20% salt solution,
  291.67 ml of 8% salt solution

• 220 ml of 20% salt solution,
  280 ml of 8% salt solution

8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time taken by the one girl alone that by one boy alone to finish the work.

• 120, 130

• 140,280

• 240,280

• 100,120

Choose the correct equations for the scenario.

A parking lot has spaces reserved for motorcycles, cars, and vans. There are five more spaces reserved for vans than for motorcycles. There are three times as many car spaces as van and motorcycle spaces combined. If the parking lot has 180 total reserved spaces, how many of each type are there?

A Bolingbrook Lady Raider basketball team has scored 54 points. Surprisingly they have only made 2pt field goals and 3pt field goals (no free throw attempts). The equation 2x + 3y = 54 represents this situation. If the team makes nine 2pt field goals, how many 3pt field goals are made?

• 12

• 9

• 10

• 11

The school that Laura goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets, 2 adult tickets and 5 child tickets for a total of $55. The school took in $67 on the second day by selling 7 senior citizen tickets, 2 adult tickets and 5 child tickets. On the third day the show earned $46 when they sold 2 senior citizen tickets, 4 adult tickets and 2 child tickets. What is the price each of one senior citizen ticket, one adult ticket and one child ticket?

• Adult: $12
  Child: $8
  Senior: $8
• Adult: $6
  Child: $4
  Senior: $5
• Adult: $7
  Child: $5
  Senior: $4
• I did not get any of the answers above so I am assuming none ofthe above.

The sum of 3 numbers is 57. The second is 3 more than the first. The third is 6 more than the first. What are the numbers in order? (Write as (x,y,z) with no spaces)

In triangle ABC, the measure of angle B is 2° more than three times the measure of angle A. The measure of angle C is 8° more than the measure of angle A. What is the measure of angle B?

Create the System of Nonlinear Equations that fits the scenario:

The ratio of two numbers is 5 to 12 and the sum of their squares is 676.

• x/y = 5/12

  x^2+y^2 = 676

• x/y = 5/12

  (x+y)^2 = 676

• x/y = 5/12

  x^2-y^2 = 676

• x/y = 5/12

  (x-y)^2 = 676

The sum of 3 numbers is 5. The first number minus the second plus the third is 1. The first minus the third is 3 more than the second. What are the numbers in order? (Write as (x,y,z) with no spaces)

The school that Laura goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets, 2 adult tickets and 5 child tickets for a total of $55. The school took in $67 on the second day by selling 7 senior citizen tickets, 2 adult tickets and 5 child tickets. On the third day the show earned $46 when they sold 2 senior citizen tickets, 4 adult tickets and 2 child tickets. What is the price each of one senior citizen ticket, one adult ticket and one child ticket?

• Adult: $12

  Child: $8

  Senior: $8

• Adult: $6

  Child: $4

  Senior: $5

• Adult: $7

  Child: $5

  Senior: $4

• None of the above.