Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Last weekend, Ann built a toolshed for her grandma. She spent half as much time building the shed on Sunday as she did on Saturday. She also spent 22 hours on Sunday organizing the tools in the shed. She ended up working the same amount of time on both days.\newlineWhich equation can you use to find hh, the number of hours Ann spent building the shed on Saturday?\newlineChoices:\newline(A) h=12h+2h = \frac{1}{2}h + 2\newline(B) h+2=12hh + 2 = \frac{1}{2}h\newlineHow many hours did Ann spend building the shed on Saturday?\newlineSimplify any fractions.\newline____ hours\newline

Full solution

Q. Last weekend, Ann built a toolshed for her grandma. She spent half as much time building the shed on Sunday as she did on Saturday. She also spent 22 hours on Sunday organizing the tools in the shed. She ended up working the same amount of time on both days.\newlineWhich equation can you use to find hh, the number of hours Ann spent building the shed on Saturday?\newlineChoices:\newline(A) h=12h+2h = \frac{1}{2}h + 2\newline(B) h+2=12hh + 2 = \frac{1}{2}h\newlineHow many hours did Ann spend building the shed on Saturday?\newlineSimplify any fractions.\newline____ hours\newline
  1. Denote hours spent: Let's denote the number of hours Ann spent building the shed on Saturday as hh. According to the problem, she spent half as much time on Sunday as she did on Saturday. This means she spent h2\frac{h}{2} hours building the shed on Sunday.
  2. Calculate total time: Additionally, Ann spent 22 hours on Sunday organizing the tools in the shed. So, the total time spent on Sunday is the time spent building the shed plus the time spent organizing, which is h2+2\frac{h}{2} + 2 hours.
  3. Set up equation: The problem states that Ann worked the same amount of time on both days. This means the time spent on Saturday (hh hours) is equal to the total time spent on Sunday (h/2+2h/2 + 2 hours). Therefore, the equation that represents this relationship is:\newlineh=h2+2h = \frac{h}{2} + 2
  4. Isolate variable: To solve for hh, we need to isolate hh on one side of the equation. We can do this by multiplying both sides of the equation by 22 to eliminate the fraction:\newline2h=h+42h = h + 4
  5. Solve for hh: Now, we subtract hh from both sides to get hh by itself:\newline2hh=h+4h2h - h = h + 4 - h\newlineh=4h = 4
  6. Final answer: We have found that Ann spent 44 hours building the shed on Saturday. This is the final answer to the problem.

More problems from Solve linear equations with variables on both sides: word problems