Marjam has a goal of taking at least 10,000 steps today. According to her pedometer, she got 2,500 steps in the morning. There are 10 hours left in the day. How many steps will she need to get each hour (assume she walks the same number of steps each hour) for the rest of the day to meet her goal? Solve this problem. If demonstrated as a number line what would said number line look like?
To find out how many steps Marjam will need to get each hour for the rest of the day, we first need to determine how many steps she still needs to reach her goal of 10,000 steps.
To do this, we subtract the number of steps she has already taken (2,500) from her goal of 10,000:
10,000 - 2,500 = 7,500 steps left to reach her goal.
Since there are 10 hours left in the day, Marjam will need to get an equal number of steps each hour to meet her goal. Therefore, we divide the number of steps left by the number of hours left:
7,500 / 10 = 750 steps per hour.
So, Marjam will need to get 750 steps each hour for the rest of the day to meet her goal of 10,000 steps.
If demonstrated as a number line, it would look like:
0 --- 2500 --- x --- x --- x --- x --- x --- x --- x --- x --- x
Each "x" represents an hour, and Marjam would need to get 750 steps during each hour to meet her goal.
would it have an open circle?
Apologies for the confusion in my previous response. In this case, since we are talking about dividing the steps evenly among the remaining hours, the number line would have closed circles to represent the total steps required each hour.
Here is how the number line would look:
0 --- 2500 --- 750 --- 750 --- 750 --- 750 --- 750 --- 750 --- 750 --- 750 --- 750 --- 750
Each closed circle represents an hour, and the number above each closed circle represents the number of steps Marjam needs to get during that hour to reach her goal. We can see that Marjam needs to get 750 steps each hour for the remaining 10 hours.
What inequality is shown on the graph (the graph is a number line with an open circle on 25.60 going into higher numbers) ? Write your inequality with the variable coming first. Use the letter m for the variable. Write your answer using a decimal number.
In this case, the number line with an open circle on 25.60 and going into higher numbers represents an inequality where the variable (m) is greater than 25.60.
The inequality can be written as:
m > 25.60
Five more than four times a number is less than 25. What are the possible values of the number?
To solve this inequality, we can set up the equation:
4x + 5 < 25
Subtracting 5 from both sides, we get:
4x < 20
Dividing both sides by 4, we have:
x < 5
So, the possible values of the number (x) would be any number less than 5, but not including 5.
Lily is saving up to buy a cellphone. She needs to save at least $300 before she is able to buy the phone. Her grandfather gives her $40, and she earns $65 tutoring after school each week. Write an inequality for the number of weeks Lily will need to save to have at least $300, and describe the solutions.
Let's denote the number of weeks Lily needs to save as 'w'.
The amount of money Lily has currently, including the amount given by her grandfather and the amount earned from tutoring each week, can be expressed as:
40 + 65w.
We can then set up an inequality to represent the condition that the total amount saved needs to be at least $300:
40 + 65w ≥ 300.
To solve this inequality, we subtract 40 from both sides:
65w ≥ 260.
Then, we divide both sides by 65 to solve for 'w':
w ≥ 4.
Therefore, Lily will need to save for at least 4 weeks in order to have at least $300.
The solution to this inequality is that 'w' (the number of weeks Lily needs to save) must be greater than or equal to 4. It is important to note that since 'w' represents a discrete quantity (whole number of weeks), the solution set consists of all whole numbers greater than or equal to 4, such as 4, 5, 6, 7, ...