Solving Systems Sums Differences

A local fish market is selling fish and lobsters by the pound. The fish costs $5.25 a pound, while the lobster costs $10.50 a pound. The fish market sells 28.5 pounds and makes $215.25?

• The market sold 16 pounds of fish and 12.5 pounds of lobster.
• The market sold 18 pounds of fish and 10.5 pounds of lobster.
• The market sold 12.5 pounds of fish and 16 pounds of lobster.
• The market sold 10.5 pounds of fish and 18 pounds of lobster.

The difference of a and b is 3. The sum of the variables is 13. Find the numbers.

• a = 7
  b = 10
• a = 8
  b = 5
• a = 10
  b = 13

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

• $5
• $10
• $15
• $20

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

A vending machine only accepts dimes and quarters. There are 85 coins in the machine with a total value of $16.75. How many of each coin are in the machine?

• 30 dimes and 55 quarters

• 55 dimes and 30 quarters

• 10 dimes and 75 quarters

• 75 dimes and 10 quarters

At a fund raising event, a booth was set up to sell handmade cards and photo frames. On the first day, 3 cards and 9 photo frames were sold for a total of $75. The next day, 8 cards and 5 photo frames were sold for a total of $67. Find the selling price of a card and the selling price of a photo frame.

• $4 photo frames and $7 cards

• $8 photo frames and $5 cards

• $4 cards and $7 photo frames

• $3 cards and $9 photo frames

A group of friend went to the mall together and got hungry so they stopped to get some snacks. Joanna and Erica bought snacks for the entire group. Joanna bought three lemonades and five pretzels for $27. Erica bought two lemonades and one pretzel and spent $11. Which system correctly displays this scenario

• 3L + 5P = 27

  2L + P = 11

• 3L + 5P = 11

  2L + P = 27

• 3L = 5P = 27

• 2L + P = 11

Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then which equations correctly display this scenario given x is fancy shirts and y is plain shirts.

• x + y = 131

  28x + 15y = 7

• x + y = 7

  28x + 15y = 131

• x + y = 131

  15x + 28y = 7

• x + y = 7

  15x + 28y = 131

There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?

• 6 pigs and 7 chickens

• 6 chickens and 7 pigs

• 0 chickens and 13 pigs

• 8 chickens and 5 pigs

Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Castel sold six apple pies and one lemon meringue pie for a total of $60. Gabriella sold one apple pie and one lemon meringue pie for a total of $20. What is the cost each of one apple pie and one lemon meringue pie?

• Apple = $12 and Lemon = $8

• Apple = $8 and Lemon = $12

• Apple = $10 and Lemon = $10

• Apple = $5 and Lemon = $15