Pregunta
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  1. You buy packs of pencils, twice as many
    packs of erasers, and three times as many
    rolls of tape. Write an expression
    in simplest form for the total
    amount of money you spent.

Ask by Sherman Wagner. in the United States
Mar 27,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

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The total amount of money spent is .

Solución

Let’s break down the problem step by step:
  1. Identify the quantities:
    • You buy packs of pencils.
    • You buy packs of erasers (twice as many as pencils).
    • You buy rolls of tape (three times as many as pencils).
  2. Define the costs:
    • Let be the price per pack of pencils.
    • Let be the price per pack of erasers.
    • Let be the price per roll of tape.
  3. Calculate the total cost:
    • The total cost for pencils is .
    • The total cost for erasers is .
    • The total cost for tape is .
  4. Combine the costs into a single expression:
  5. Factor out :
Thus, the expression for the total amount of money spent in simplest form is:

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Extra Insights

To find the total cost, we can assign variables to the prices of the items: let the price of one pack of pencils be , the price of one pack of erasers be , and the price of one roll of tape be . Therefore, the total amount you spend can be expressed as:
So the expression for the total spent is .
Knowing how to derive expressions like this can be very useful not just in math, but in real-life budgeting! Whenever you need to keep track of multiple items and their quantities, using variables can help clarify your expenses. Plus, being able to model your spending habits means you can plan more effectively for future purchases.
Mathematics also plays a crucial role in various fields! For instance, in manufacturing, a similar approach might be used to manage inventory and forecast costs by categorizing materials and their respective prices. Understanding how variables interact can streamline production and save businesses money in the long run.

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