Misc.
Elijah is 28 years old. He is 12 years older than 2/3 of Laurel’s age. Which equation can be used to find Laurel’s age, a?
2/3a + 12 = 28
−4/3 (r + 3) = −2
r = -1 1/2
Solving Equations
5 + 5x - 1 = 29
x = 5
2(x - 4) = 5x + 4
x = -4
The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for 9 days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of $25 applied to their rental cost. The Logans will pay $920 in all.
What equation can you write to find d, how much the agency charges per day?
9d - 25 = 920
Will this equation have no solution, one solution, or infinitely many solutions
4(x − 3) = 1/2 ( x/2 + 5)
One solution
Solving Equations
x + 3 + 3x = 7
x = 1
4x - 2 = 3x + 5
x = 7
Estelle is having her birthday party at Gold Frames Art Museum this year. A party package costs $265 and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her 8 guests, bringing the total to $305.
Write an equation to find f, the cost of each favor?
8f + 265 = 305
Complete the equation so that it has infinitely many solutions.
4(x/8 − 2) = 1/4 (2x − ____)
32
3x − 4 = 2x − 2 + x
No Solution
Solving Equations
-45 = 3x + 4 + 4x
x = -7
x = 4
Isaiah spent his first 4 tokens at Zap Zoo Arcade on a game of air hockey. Then he played his favorite game, Solar Scout, over and over until he ran out of tokens. Solar Scout costs 2 tokens per game, and Isaiah started with a bucket of 40 game tokens. How many games of Solar Scout did Isaiah play?
18 games
Gwen saves 15% of her income. This month her income is $500 more than last month. The expression 0.15(x + 500) represents the amount of money she saves this month, where x is last month’s income. Gwen saves $210 this month. What was Gwen’s income in dollars last month?
$900
3(4 − 2x) = 6(−x + 2)
Infinite solutions
Solving Equations
14 = -(2a + 6) + 2
a= -9
x = 1
Zack sold 3 of his old hockey sticks at Refreeze Secondhand Sports Shop. Before he left, he spent $25 of his earnings on a used pair of hockey gloves. He had $71 remaining. How much did Zack receive for each hockey stick?
$32
Ricardo is considering two monthly plans a dog-walking service offers.
• Plan 1 charges $3 per walk plus $10 for grooming at the end of each month.
• Plan 2 charges $5 per walk and then offers free grooming at the end of each month.
Write an equation to model the number of walks, w, when the two plans cost the same amount.
3w + 10 = 5w
−3/4 (x − 3) − 5 = 1/8 (x − 1)
x = -3
Solving Equations
-21 = 7(5k - 8)
k = 1
6x - 15 + 4x = 5(2x - 3)
Infinite Solutions
Valeria has been training for the Charlestown Cruisers bike race. The first week she trained, she rode 5 days and took the same two routes each day. She rode an 8-mile route each morning and a longer route each evening. By the end of the week, she had ridden a total of 115 miles. How many miles did Valeria ride each evening?
Write your answer as a whole number or a decimal.
15 miles