Solving Systems of Equations Word Problems Unit 2 Day 3
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: Travis and his band are planning to record their first CD. The initial start-up cost is $1500, and each CD will cost $4 to produce. They plan to sell their CDs for $10 each. How many CDs must the band sell before they make a profit?
x represents: ______y represents: ______
Equation 1: Cost to produce CD ______(x, y) answer: ______
Equation 2: Income from selling CDs ______Word Answer: ______
Example 2: Laura’s Copies has two options for buying photocopies. With Option 1, you can buy a card for $40 each year and then pay $0.03 per copy. With Option 2, you can just pay $0.05 per copy. For how many copies would the cost of Options 1 and 2 be the same? What is the cost?
x represents: ______y represents: ______
You Try! Jorge’s school is selling tickets to the spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of one senior citizen ticket and one child ticket?
x represents: ______y represents: ______
You Try! The Waxman’s just opened a carpet store. Their startup costs were $5000, and their cost of carpet is $8 per square yard. How many square yards of carpet do they need to sell in order to break even if they sell the carpet for $18 per square yard?
Solving Three Variable Systems of Equations
You can solve three 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?
x represents: ______y represents: ______z represents: ______
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?
x represents: ______y represents: ______z represents: ______
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?