Answered

Dontavious has a box of colored pencils. He uses 53 pencils and has 118 pencils left in the box. Write an equation showing how many pencils were in the box before he started drawing.


A$53+p=118$
B$118+p=53$
C$p-53=118$
D$p=118-53$

Verified Answer :

  • Define the initial number of pencils as \(p\).
  • Identify that removing 53 pencils from the initial total leaves 118 pencils.
  • Formulate the equation based on this relationship: \(p - 53 = 118\).
  • The correct option is \(\boxed{p - 53 = 118}\).

Explanation

  1. Understanding the Problem

The problem asks for an equation to represent the initial number of pencils in a box, given that 53 pencils were used and 118 pencils remain. Let \(p\) represent the initial number of pencils in the box before Dontavious started using them. When a quantity of items is removed from an initial total, we subtract that quantity from the initial amount to find the remainder. Here, the amount removed is 53, and the remainder is 118.

  1. Formulating the Equation

Based on our analysis, we have the initial quantity \(p\). Subtracting the 53 pencils that were used gives the remaining 118 pencils. This relationship can be expressed by the equation:
\[p - 53 = 118\]
This equation states that the initial amount, minus the amount used, is equal to the amount left over.

  1. Selecting the Correct Option

Comparing our derived equation \(p - 53 = 118\) with the provided options:

  1. \(53 + p = 118\) (Incorrect: This implies the initial amount plus the used amount equals the remaining amount, which is not logical here.)
  2. \(118 + p = 53\) (Incorrect: This is not consistent with the subtraction relationship.)
  3. \(p - 53 = 118\) (Correct: This matches our derived equation.)
  4. \(p = 118 - 53\) (Incorrect: This would mean the total number of pencils is the difference between the remaining amount and the used amount, which is not correct.)

Therefore, the correct equation is \(p - 53 = 118\).

Examples

This type of algebraic modeling is fundamental in managing resources. For example, if you have a certain amount of budget for a month, and you spend a portion of it on groceries, you can use an equation like \(\text{Initial Budget} - \text{Grocery Spending} = \text{Remaining Budget}\) to keep track of your finances. This helps in understanding how individual transactions impact your overall total and is a great way to apply basic algebra to everyday tasks like planning expenses or inventory management.

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