Word Problems
Naomi and Shelley both hiked the Discovery Point trail. When Shelley started hiking, Naomi was already 1.3 miles from the trailhead, walking at a rate of 2.4 miles per hour. Shelley started at the trailhead and jogged at a rate of 5 miles per hour.
How long did it take Shelley to catch up to Naomi?
0.5 hours
Alexis and her little sister Emma went to Gold Trust National Bank. When they got there, Alexis had three times as much money in her account as Emma. After Alexis withdrew $100 to buy some new clothes and Emma deposited $25 that she got for her birthday, they had the same amount in their accounts.
How much money did Emma have in her account when she and Alexis got to the bank?
$62.50
At the Adventure Arena amusement park, people can ride the G-Force roller coaster forward or backward. Each train has 15 forward-facing seats and 9 backward-facing seats. Last night, when the lines closed to new riders, 130 people were in line to ride forward and 100 people were in line to ride backward.
If the train was completely full for each ride, how many rides did it take for the lines to have the same number of people?
5 rides
Ed is booking a hotel room for his vacation. If he stays for 7 nights, the hotel will give him a $280 discount. He notices that the amount he would pay for 7 nights with the discount is the same as the amount he would pay for 5 nights without the discount.
What is the full price of the hotel room per night?
$140
Ann is starting a digital art business. She spends $89 on software and $394 on online advertisements. Printing and framing each piece of art will cost her $14, and she will sell each piece for $35.
Which equation can you use to find a, the number of pieces of art Ann must sell for her sales to equal her expenses?
35a = 89 + 394 + 14a
After graduation, Rob got job offers from two different companies. Printer Palace offered him $3,500 per month, plus a $7,000 signing bonus. East Company Paper offered him $4,500 per month, with no signing bonus.
How many months would Rob need to work for his total earnings to be the same at either company?
7 months
Tom was playing fetch in the park with his Jack Russell terrier. On one throw, the ball landed 90 meters from the terrier, and the terrier started running toward it at 11 meters per second. At the same time, a greyhound that was 140 meters away from the ball started running toward it at a speed of 19 meters per second.
If each dog kept a constant speed, how long did it take for both dogs to be the same distance from the ball?
Simplify any fractions.
25/4
John is wrapping tamales. He has already wrapped 6 tamales when his friend Cole arrives to help. John wraps 2 tamales every minute, and Cole wraps 3 tamales every minute.
At this pace, how many minutes will it take for Cole to have wrapped the same number of tamales as John?
Simplify any fractions.
6 minutes
Tanner and his sister, Mona, both brought gummy bears on a family car trip. At the beginning of the drive, Mona had twice as many gummy bears as Tanner. While on the road, Mona ate 23 of her gummy bears and Tanner ate 7 of his. When they got to their destination, Tanner realized they each had the same number of gummy bears left.
Which equation can you use to find t, the number of gummy bears Tanner had at the beginning of the drive?
2t - 23 = t - 7
Ann is starting a digital art business. She spends $89 on software and $394 on online advertisements. Printing and framing each piece of art will cost her $14, and she will sell each piece for $35.
How many pieces of art must Ann sell for her sales to equal her expenses?
23 pieces
Tina and Shane waited in line all day at Get 'Em Games to buy the new PowerPlay3000 gaming system. Shane got his system for $250.50, and he bought 2 controllers to go with it. Tina, a Get 'Em Games Gold Member, got her system for only $200, and she bought 4 controllers at regular price. Tina and Shane each spent the same amount in total.
Which equation can you use to find c, the cost of each controller?
250.50 + 2c = 200 + 4c
Ken is comparing the cost of two different food-delivery apps. The total amount the apps charge depends on how far Ken's home is from the restaurant. One app charges $0.50 per mile, plus a $3 service fee. The other charges $0.75 per mile, with no additional fee.
How far from Ken's home would a restaurant need to be for the two options to cost the same?
Simplify any fractions.
12 miles
One morning in Austin, Texas, the temperature was 80°F and rose by 2°F per hour until midafternoon. At the same time in Little Rock, Arkansas, the temperature was 72°F and rose by 4°F per hour. Which equation can you use to find h, the number of hours it took for the cities to reach the same temperature?
80 + 2h = 72 + 4h
Tanner and his sister, Mona, both brought gummy bears on a family car trip. At the beginning of the drive, Mona had twice as many gummy bears as Tanner. While on the road, Mona ate 23 of her gummy bears and Tanner ate 7 of his. When they got to their destination, Tanner realized they each had the same number of gummy bears left.
How many gummy bears did Tanner have at the beginning of the drive?
16 gummy bears
Ezra and Leah took their families to the movie theater last weekend, and they each spent the same amount of money. Ezra bought 5 tickets and spent $12 on popcorn, while Leah bought 3 tickets and spent $24 on popcorn plus $9 on sodas.
Which equation can you use to find p, the price of each movie ticket?
5p + 12 = 3p + 24 + 9
Tina and Shane waited in line all day at Get 'Em Games to buy the new PowerPlay3000 gaming system. Shane got his system for $250.50, and he bought 2 controllers to go with it. Tina, a Get 'Em Games Gold Member, got her system for only $200, and she bought 4 controllers at regular price. Tina and Shane each spent the same amount in total.
How much did each controller cost?
$25.25
Scarlett and Tristan are both running for student council president. At the start of the last day of voting, Tristan had half as many votes as Scarlett. Throughout the day, Scarlett gained 11 more votes, while Tristan gained 34 more votes. By the end of the day, Scarlett and Tristan had the same number of votes.
How many votes did Scarlett have at the start of the last day of voting?
46 votes
One morning in Austin, Texas, the temperature was 80°F and rose by 2°F per hour until midafternoon. At the same time in Little Rock, Arkansas, the temperature was 72°F and rose by 4°F per hour.
How long did it take for the cities to reach the same temperature?
Simplify any fractions.
4 hours
Brett and Kenny work the same weekend shifts at Cool Beans Coffee Co. Kenny is a new employee and earns $10 per hour, while Brett has more experience and earns $12.50 per hour. Kenny also received a $75 bonus at the beginning of the month for joining the company.
Which equation can you use to find h, the number of hours Brett and Kenny need to work to earn the same amount of money this month?
75 + 10h = 12.5h
Ezra and Leah took their families to the movie theater last weekend, and they each spent the same amount of money. Ezra bought 5 tickets and spent $12 on popcorn, while Leah bought 3 tickets and spent $24 on popcorn plus $9 on sodas.
What was the price of each movie ticket?
$10.50
Two stores were selling pumpkins on the first day of October. The first store had 190 pumpkins in stock when it opened and sold 10 pumpkins every hour. The other store had 164 pumpkins when it opened and sold 6 pumpkins every hour. The two stores opened at the same time.
How many hours after opening did it take for the two stores to have the same number of pumpkins?
Simplify any fractions.
13/2
Beth is buying coffee for everyone in her study group. If she goes to the café next to her school, it will cost her $3.25 per coffee. If she goes to the café by her home, it will cost her $3.75 per coffee, but she has a coupon for $5 off.
How many coffees would Beth need to buy for the two options to cost the same?
10 coffees
Ed is booking a hotel room for his vacation. If he stays for 7 nights, the hotel will give him a $280 discount. He notices that the amount he would pay for 7 nights with the discount is the same as the amount he would pay for 5 nights without the discount.
Which equation can you use to find p, the full price of the hotel room per night?
7p - 280 = 5p
Brett and Kenny work the same weekend shifts at Cool Beans Coffee Co. Kenny is a new employee and earns $10 per hour, while Brett has more experience and earns $12.50 per hour. Kenny also received a $75 bonus at the beginning of the month for joining the company.
How many hours will Brett and Kenny need to work to earn the same amount of money this month?
Simplify any fractions.
30 hours
Last Saturday, Erin and Krysta each biked the Prairie Point Trail, a 20-mile path leading to the peak of Prairie Point Mountain. Both girls started at 7:00 A.M., heading toward the peak. Erin started at the trailhead and biked at a constant speed of 10 miles per hour. Krysta started at an entry point 3 miles ahead of the trailhead and rode at a steady pace of 8 miles per hour.
If each girl kept a constant speed, which equation can you use to find h, the number of hours it took for Erin to catch up to Krysta?
10h = 8h + 3