Lesson 6: System of linear equations word problems

At a fruit stand, you notice the person in front of you gets 5 apples and 4 oranges for $10. You get 5 apples and 5 oranges for $11

Write 2 equations for this problem (let x be apples and y be oranges)

Person: 5x + 4y = 10

You: 5x + 5y = 11

At a fruit stand, you notice the person in front of you gets 5 apples and 4 oranges for $10. You get 5 apples and 5 oranges for $11

Write 2 equations for this problem (let x be apples and y be oranges). THEN, solve and see how much an apple and orange is together

$1.20

An electronic piggybank shows the total amount of money in it, as well as the total number of coins in it. The display reads: $2 and 16 coins

Write 2 equations for this problem (let n be nickels and q be quarters)

n + q = 16

0.05n + 0.25q = 2

An electronic piggybank shows the total amount of money in it, as well as the total number of coins in it. The display reads: $2 and 16 coins

Write 2 equations for this problem (let n be nickels and q be quarters). Then solve to find the total number of nickels and quarters

10 nickels and 6 quarters

Word problems that require us to write systems of linear equations have ___ unknown quantities and ___ different ways to relate them

two, two

How do you know if a word problem is a system of linear equations?

If it’s asking for two or more unknown values/two or more separate conditions linking them together

In a system of linear equations, both equations have to have the same what?

Variables

A theater charges $21 for adult tickets and $15 for student tickets. The theater sold 102 tickets on opening night and made $1,932 in ticket sales

Write 2 equations for this problem (let a be adult tickets and s be student tickets)

a + s = 102

21a + 15s = 1,932

A theater charges $21 for adult tickets and $15 for student tickets. The theater sold 102 tickets on opening night and made $1,932 in ticket sales

Write 2 equations for this problem (let a be adult tickets and s be student tickets). Then solve to find how many of each tickets were sold

67 adult tickets and 35 student tickets

A player of a trivia game receives 100 points for each correct answer and loses 25 points for each incorrect answer. Leona answered a total of 30 questions and scored a total of 2,125 points

Write 2 equations for this problem (let c be correct and i be incorrect answers)

c + i = 30

100c - 25i = 2,125

Mike and Sally are teachers at the same school. Mike has 6 more years of teaching experience, and the two of them have 16 years of teaching experience combined

Write two equations (let m be Mike and s be Sally)

m = 6 + s

m + s = 16

Mike and Sally are teachers at the same school. Mike has 6 more years of teaching experience, and the two of them have 16 years of teaching experience combined

Write two equations (let m be Mike and s be Sally) and solve to see how many years of teaching experience Sally has

5

Hazel and Leo are comparing the number of keys on their keychains. Leo has 4 more keys than Hazel, and the two of them have 18 keys combined

Write 2 equations (let h be hazel and l be leo)

l = 4+ h

l + h = 18

Hazel and Leo are comparing the number of keys on their keychains. Leo has 4 more keys than Hazel, and the two of them have 18 keys combined

Write 2 equations (let h be hazel and l be leo) then solve to find out how many keys Hazel has

7