Linear Equations Word Problems

On the windowsill is a plant that is 15 centimetres tall. It is growing 2 centimetres per week. A second plant, which is 5 centimetres tall, is on the coffee table. It is growing 4 centimetres per week. Eventually the two plants will be the same height. How many weeks will that take?

• 5 weeks

• 25 weeks

• 10 weeks

• 2 weeks

Pam and her friend Meg are knitting scarves for the homeless. Pam had already completed 10 scarves and has committed to making 3 more scarves per day. Meg, who hasn't completed any scarves yet, has more free time and can make 4 scarves per day. At some point, Meg will catch up and they will both have completed the same number of scarves. How many scarves will each woman have finished?

• 10 days

• 10 scarves

• 40 scarves

• 40 days

Ron and his cousin Kate are picking apples in their grandparents' orchard. Ron has filled 10 baskets with apples and is filling them at a rate of 6 baskets per hour. Kate has 5 full baskets and will continue picking at 7 baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take?

• 40 baskets

• 40 hours

• 5 baskets

• 5 hours

Terrence just got his commercial driver's licence and is starting a new career as a truck driver. Getting trained and licenced involved a one-time cost of $500. Fuel and insurance end up costing him $4 per km. For his first delivery, Terrence will get paid $400 plus $8 per km that he drives. If he drives a certain distance on this delivery, Terrence will break even, making back all the money he had to spend. How much would both the costs and the earnings be?

• 25 km

• $600

• $25

• 600 km

Yesterday, two friends went into a bank to open savings accounts. Carmen started by putting $60 in her account, and she will deposit an additional $4 each week. Zack made no initial deposit, but he will add $16 more each week. In a few weeks, the friends will have the same account balance. What is that account balance?

• 80 weeks

• $80

• 5 weeks

• $5

Kaylee's Bakery recently spent a total of $300 on new equipment, and their average hourly operating costs are $10. Their average hourly receipts are $20. The bakery will soon make back the amount it invested in equipment. How many hours will that take?

• 30 hours

• $30

• $600

• 600 hours

The members of a cooking club are making cakes, which they will sell at a street fair for $10 a piece. It cost $50 for a booth at the fair, and the ingredients for each cake cost $5. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How many cakes will they have sold?

• $10

• 100 cakes

• $100

• 10 cakes

Rachel and her sister Beth are making baby blankets to sell at a boutique. Rachel has already completed 5 blankets and can finish 1 more blanket per day. Beth has already completed 2 blankets and can finish 2 more blankets per day. At some point, they will have completed the same number of blankets. How many blankets will each woman have made?

• 3 days

• 8 blankets

• 8 days

• 3 blankets

Mrs. Wilkinson, the P.E. teacher, is pairing off students to race against each other. Jill can run 6 metres per second, and Sandra can run 8 metres per second. Mrs. Wilkinson decides to give Jill a head start of 50 metres since she runs more slowly. Once the students start running, Sandra will quickly catch up to Jill. How far will Sandra have to run?

• 200 metres

• 25 seconds

• 25 metres

• 200 seconds

Two classmates, Allie and Vincent, plan to meet in the computer lab to type up their research papers. Allie can type at a speed of 1 page per hour, whereas Vincent can type 2 pages per hour. So far, Allie already has 8 pages typed up, compared to Vincent's 6 pages. Once they sit down and start typing together, the two students will reach the same page count before too long. How long will that take?

• 2 hours

• 10 pages

• 2 pages

• 10 hours