Unit 1 Day 6: Solving Systems of Equations Word Problems
Name: ____________________
Solving Two Variable Systems of Equations
You can solve two variable systems word problems by following these steps:
1. Read the problem and underline (or highlight) the question.
2. Define the variables!
3. Read over the problem again. Anytime you see the word representing your variable, substitute your
variable into the equation!
4. Remember: Two variables means there will be two equations!
Example 1: If 8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10, how much does each pen and
each pencil cost?
Example 2: Last Monday, an airline flew 89 passengers on a commuter flight from Boston to New York. Some of
the passengers paid $120 for their tickets and the rest paid $230 for their tickets. The total cost of all of the
tickets was $14,200. How many passengers bought $120 tickets? How many bought $230 tickets?
You Try! On Saturday, Mrs. Bouskill bought 2 lbs of bananas and 4 lbs of tofu and spent $6.40. If the tofu costs
6 times more than the bananas per pound, how much does one pound of bananas and one pound of tofu cost?
Challenge
You Try! A student has some $5 bills and $20 bills in his wallet. He
has a total of 13 bills that are worth $140. How many of each type of
bill does he have?
A kayaker can paddle 12 mi in 2 hours
moving with the river current. Paddling
at the same pace, the trip back against
the current takes 4 hours. Assume that
the river current is constant. Find what
the kayaker’s speed would be in still
water.
Solving Three Variable Systems of Equations
You can solve two variable systems word problems by following these steps:
1. Read the problem and underline (or highlight) the question.
2. Define the variables!
3. Read over the problem again. Anytime you see the word representing your variable, substitute your
variable into the equation!
4. Remember: Three variables means there will be three equations!
Example 3: You have 17 coins in pennies, nickels, and dimes in your pocket. The value of the coins is $0.47. There
are four times the number of pennies as nickels. How many of each type of coin do you have?
Example 4: For a party, you are cooking a large amount of stew that has meat, potatoes, and carrots.
The meat costs $6 per pound, the potatoes cost $3 per pound, and the carrots cost $1 per pound. You
spend $48.50 on 13.5 pounds of food. You buy twice as many carrots as potatoes. How much of each
ingredient did you buy?
You Try! You work at a fruit stand that sells apples for $2 per pound,
oranges for $5 per pound, and bananas for $3 per pound. Yesterday
you sold 60 pounds of fruit and made $180. You sold 10 more pounds
of apples than bananas.
a. Write a system of equations representing the information above.
b. How many pounds of each kind of fruit did you sell yesterday?
c. What kind of fruit did you sell the most?
Challenge
A worker received a $10,000 bonus and
decided to split it among three different
accounts. He placed part in a savings
account paying 4.5% per year, twice as
much in government bonds paying 5%, and
the rest in a mutual fund that returned
4%. His income from these investments
after one year was $455. How much did
the worker place in each account?