Equations Problems

The length of a rectangle is 3 times its width. If the width is increased by 2 cm and the length is increased by 4 cm, its area will be doubled. Find the original dimensions of the rectangle.

• 7cm by 21cm

• 6cm by 18cm

• 5cm by 15cm

• 4cm by 12cm

Each month, Olin’s cell phone plan costs $34.99, plus $12.95 per GB of data that he uses. His bill this month was $60.89. Which equation can be used to find the amount of data (d) Olin used this month?

• 34.99d +12.95 = 60.89

• 34.99 + d = 60.89

• 34.99 - 12.95d = 60.89

• 34.99 + 12.95d = 60.89

A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. What is the y-intercept in context.

• The additional fee of $8.

• The initial fee of $25.

• The additional fee of $25.

• The initial fee of $8.

In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation that models this situation.

• y = 20x + 5

• y = 5x + 20

• y= -5x + 20

• y = 5x - 20

Toby is buying pet supplies for his dog. He purchases 3 bags of treats and x bags of dog food. The treats were on sale for $4.50 each. The bags of food were $26 each. Which equation can be used to determine the total amount of money Toby spent on supplies for his dog.

• y = 13.50 + 26x

• y = 3x + 30.50

• y = 4.50 + 26x

Which situation can be represented by the equation y = 8x + 42.5

• Emily plans to take art classes to learn how to paint. She spends $42.50 on supplies at Hobby Lobby and $8.00 on supplies at Michaels. What is y, the total amount spent after buying x supplies?

• Ari has $42.50 in her bank account. She spends $8.00 on Christmas gifts for each of her AVID mentees. How much total money, y, does Ari have in her account after buying x, gifts?

• Christine buys some movie tickets for $8.00 each. Then she spends $42.50 on snacks at the concession stand. What is y, the total amount spent after buying, x, tickets?

• Stephen is a baker and sells birthday cakes. He spends $42.50 on ingredients, then charges $8.00 per cake. What is y, the total amount earned after selling x, cakes?

The temperature where Cally lives is 73℉ and is falling 2℉ per hour. Which of the following equations can be used to determine how many hours (h) it will take for the temperature to drop to 65℉?

• 73 - 2h = 65

• 73 - 65 = 2h

• 65 - 2h = 63

• 2h - 73 = 65

Haylee is on page 219 of her library book. She reads at a pace of 1.5 pages per minute. Which of the following equations could be used to determine the total pages read (y) after a given number of minutes (x)?

• y = 219x + 1.5

• 219 = y +1.5x

• y = 1.5x +219

• y = 220.5x

Five less than twice a number is equivalent to 47. 

• 5 - 2x = 47 

• 2x - 5 = 47 

• 5x - 2 = 47 

• 2 - 5x = 47 

10 less that half a number is equivalent to 8.  

• 10 - 1⁄2x = 8 

• 1⁄2x + 10 = 8

• 1⁄2x - 10 = 8

• 10x - 0.5 = 8