Solving Word Problems Algebraically Using a System of Equations

Solving Word Problems Algebraically using a System of Equations

Solve each word problem algebraically by setting up a system of equations.

1) The difference of two numbers is 3. Their sum is 13. Find the numbers.

2) A large group of students wants to go to the movies. If the students take 3 vans and 1 car, they can transport 22 people. If they take 2 vans and 4 cars, they can transport 28 people. Find the number of people that can be transported in a van and in a car.

3) The difference between two numbers is 2. When the sum of the smaller number and 3 is multiplied by 3, the result is equal to two times the sum of the larger number and 2. Find the numbers.

4) Rob invested $12,500, part at 4% and part at 6%. He earned $652 from the two investments. How much money did he invest at each rate?

5) A sophomore class raised $860 from the sale of tickets to a concert. Tickets sold for $2.50 if purchased in advance and for $4.00 if purchased at the door. If a total of 275 tickets were sold, what was the number of tickets sold at the door?

6) You have a total of 18 coins. Some are nickels and the rest are dimes. If the value of the coins is $1.25, how many of each coin do you have?

7) Tickets for the school play sell for $3 per student and $5 per adult. One night, 595 people bought tickets. The school took in $1951. How many adult tickets were sold?

8) An amusement park charges admission plus a fee for each ride. Admission plus two rides costs $10. Admission plus five rides costs $16. What is the charge for admission? For each ride?

9) The Town Recreation Department ordered 100 baseballs and bats for the summer baseball camp for $822. The baseballs cost $4.50 each and the bats cost $20 each. How many of each item were ordered?

10) Carrie invested $20,000, some at 3% and the rest at 2%. The money earned from each part was equal. Find the amount invested at each rate.

11) Cedric and Zelda went shopping at Price Buster. Cedric bought 2 jumbo rolls of aluminum foil and 3 packages of AA batteries for a total cost of $21. Zelda bought 5 identical jumbo rolls of aluminum foil and 2 identical packages of AA batteries for a total cost of $25. Find the cost of 1 jumbo roll of aluminum foil and the cost of 1 package of AA batteries.

12) Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.

13) Membership at Synergy Gym is $50 per month plus a one-time registration fee of $150. Membership at Gold’s Gym is $70 per month plus a one-time registration fee of $90. After how many months will the membership costs be the same at both gyms? What will the cost be? Which gym is more cost effective? Explain.