Real World Application System of Equations

SOLVE the SYSTEM:

José and Jorge sell mango and guavas at their fruit stand.

When you arrive to sell fruit for them, you realize that they never told you what the prices were and there is no sign.

You see two orders that you can use to figure out the two unknown prices.

1 mango and three guavas cost $12, and 2 mangos and 1 guava cost $5.

How much do the mangoes and guavas cost?

• Mangoes are $0.60 each.

  Guavas are $3 each.

• Mangoes are $2.50 each.

  Guavas are $4 each.

• Mangoes are $3 each.

  Guavas are $2.50 each.

• Mangoes are $3.80 each.

  Guavas are $0.60 each.

• Mangoes are $0.60 each.

  Guavas are $3.80 each.

Answer explanation

Tags

F-LE.1

What is the 1st step to solving a real-world application problem of systems?

• Solve the system using the Substitution or Elimination

• Write 2 linear equations to create a system

• Define the variables (x and y)

• Write answers with labels (in context of the problem)

Answer explanation

Tags

F-LE.1

Which methods can be used to SOLVE a systems application problem?

• Graphing method

• Substitution method

• Elimination method

• None of these methods

Answer explanation

Tags

F-LE.1

1) Define the variables for the system:

When you get insurance on your home, you have the option to add extra insurance for very valuable items like jewelry and art.

You find that your insurance company charges a flat fee plus a percentage of the value of the item.

It costs $39 to insure a $1200 and $77 to insure a $3100 item.

What are the flat fee and percentage charges?

• x = # of jewelry items

  y = # of art pieces

• m = flat rate

  b = percentage

• x = insurance premium

  y = value of item

• m = percentage rate

  b = flat fee

• x = home insurance

  y = extra insurance

Answer explanation

Tags

F-LE.1

WRITE 2 EQUATIONS for the SYSTEM:

When you get insurance on your home, you have the option to add extra insurance for very valuable items like jewelry and art.

You find that your insurance company charges a flat fee plus a percentage of the value of the item.

It costs $39 to insure a $1200 and $77 to insure a $3100 item.

What are the flat fee and percentage charges?

• x = 39m + 1200

  y = 77m + 3100

• 39x + 77y = 116

  1200x + 3100y = 4500

• 39x + 1200 = b

  77x + 3100 = b

• 1200 = 39m + b

  3100 = 77m + b

• 39 = 1200m + b

  77 = 3100m + b

Answer explanation

Tags

F-LE.1

When you get insurance on your home, you have the option to add extra insurance for very valuable items like jewelry and art.

You find that your insurance company charges a flat fee plus a percentage of the value of the item.

It costs $39 to insure a $1200 and $77 to insure a $3100 item.

What are the flat fee and percentage charges?

• The flat fee is $15.

  The percentage charge is 2% of the value of the item.

• The percentage charge is 15% of the value of the item.

  The flat fee is $2.

• The percentage charge is 3.25% of the value of the item.

  The flat fee is $2.48.

• The flat fee is $3.25.

  The percentage charge is 2.48% of the value of the item.

• The flat fee is $50.

  The percentage charge is 30% of the value of the item.

Answer explanation

Tags

F-LE.1

At Whole Foods, you can purchase 3 pounds of raspberries and 5 pounds of strawberries for $42. You can purchase 5 pounds of raspberries and 3 pounds of strawberries for $38. Which system of equations below could be used to find out the price of each pound of raspberries and strawberries?

• 3r + 5s = 42

  5r + 3s = 38

• 3r - 5s = 42

  5r - 3s = 38

• 3r + 3s = 42

  5r + 5s = 38

• 5r + 5s = 42

  3r + 3s = 38

At Whole Foods, you can purchase 3 pounds of raspberries and 5 pounds of strawberries for $42. You can purchase 5 pounds of raspberries and 3 pounds of strawberries for $38. What is the price for each pound of strawberries?

• Each pound of strawberries costs $3.

• Each pound of strawberries costs $4.

• Each pound of strawberries costs $5.

• Each pound of strawberries costs $6.

The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior tickets and 5 student tickets. Which system of equation listed below could be used to solve the price of each senior and student ticket?

• 4c + 5s = 102

  7c + 5s = 126

• 7c + 5s = 102

  4c + 5s = 126

• 4c - 5s = 102

  7c - 5s = 126

• 7c - 5s = 102

  4c - 5s = 126

The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales, the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior tickets and 5 student tickets. Which answer below shows the correct price of each senior citizen ticket and each student ticket?

• $8 for a senior ticket, $12 for a student ticket

• $8 for a senior ticket, $14 for a student ticket

• $12 for a senior ticket, $8 for a student ticket

• $14 for a senior ticket, $8 for a student ticket