For each problem, complete each of the following:
• define your two variables.
• write a system of equations.
solve the system, showing all work.
write your final answer as a complete sentence that answers the question.
1. in a jar, the number of blue marbles equals twice the number of red marbles. there are 24 more blue
marbles than red marbles. how many red and blue marbles are in the jar?
2. in another jar, there are eight times as many purple marbles as there are yellow marbles. in all, there are
153 marbles. how many purple and yellow marbles are in the jar?
3. on uncle ted's farm, he raises cows and ducks. each cow has 4 legs and each duck has 2 legs. there are
128 legs and 52 animals on the farm. how many cows and ducks are on the farm?
4. at the burger shed, a hamburger costs twice as much as fries. alice bought 3 burgers and 5 fries for a total
of $27.50. what is the cost of each item?
5. meow 'n' more pet store sells cats and birds. cats have 4 legs and birds have 2. there are 37 animals and
116 legs in the store. how many of each animal are there?
6. while playing skyrim, dwight collects several dragon scales and dragon bones. each dragon scale is worth
250 gold and each dragon bone is worth 500 gold. if he has collected a total of 11 dragon items that are
worth a total of 3750 gold, then how many of each item did dwight collect?
7. two families go to a baseball game. one family purchases two adult tickets and four youth tickets for $58.
another family purchases four adult tickets and five youth tickets for $90.50. find the cost of one adult
ticket and one youth ticket.
8. during a football game, the booster club sells pretzels and popcorn to raise money for new uniforms. they
charge $2.50 for a bag of popcorn and $2 for a pretzel. the parents collect $35 in sales during the game.
they sell twice as many bags of popcorn as pretzels. how many bags of popcorn did they sell? how many
pretzels did they sell?