Answer:
Liam's remaining amount: $250 - ($p / 24)
h = 10
Explanation:
Liam's Remaining Amount:
Background information:
We know that:
- Liam initially has $250,
- and that the cost of the present was evenly split among 24 people, including Lia
Cost per person:
The cost per person the total cost divided by the number of people:
Cost per person = Total cost / Number of people
Since the cost is represented by $p and the number of people is 24, we have:
Cost per person = $p / 24
Determining the amount of money Liam has left:
- Liam is included among the 24 people, so he also paid the cost per person for the present.
Thus, we can determine how much money he has left by subtracting the cost per person from his initial amount:
Liam's remaining amount = Initial amount - Cost per person
Liam's remaining amount = $250 - ($p / 24)
Therefore, the expression we could use to determine Liam's remaining amount is $250 - ($p / 24).
-----------------------------------------------------------------------------------------------------------
Solving for h:
Step 1: Multiply each fraction by the least common denominator (LCD) to clear the fraction:
- The least common denominator (LCD) is the smallest number that can be evenly divided by all the denominators.
- Out of the three denominators (7, 14, and 7), 14 is the LCD.
Thus, we can multiply each fraction by 14 to clear the fractions:
Multiplying 3/7 by 14:
3/7 * 14
42/7
6
Multiplying h/14 by 14:
h/14 * 14
14h/14
h
Multiplying -2/7 by 14:
-2/7 * 14
-28/7
-4
Thus, our new equation is given by:
6 = h - 4
Step 2: Solve for h by adding 4 to both sides:
(6 = h - 4) + 4
10 = h
Thus, h = 10.
Optional Step 3: Check the validity of the answer:
We can check that our answer is correct by plugging in 10 for h and seeing if we get 3/7 on both sides of the equation:
3/7 = 10/14 - 2/7
3/7 = 5/7 - 2/7
3/7 = 3/7
Thus, our answer is correct.