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Chapter 2: Problem 62

Claire has \(y\) dimes. Express the value of the dimes in cents.

Short Answer

Expert verified
10y cents.

Step by step solution

01

Understand the value of a dime

A single dime is worth 10 cents.
02

Multiply the value of one dime by the number of dimes

If Claire has \( y \) dimes and each dime is worth 10 cents, the total value in cents can be found by multiplying the number of dimes by the value of one dime: \( 10 \times y \).
03

Express the total value in an equation

The total value of \( y \) dimes in cents is expressed as \( 10y \) cents.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Value of Dimes
To understand the value of the dimes Claire has, we need to know what a dime is worth.
In the United States, a single dime equals 10 cents.
This is a fixed value and does not change.
Knowing this, we can calculate the total value of multiple dimes.
For instance, if you have 5 dimes, their total value is: 5 dimes 脳 10 cents = 50 cents.
Multiplication
Multiplication is a mathematical operation used to calculate the total value of several equal parts.
In our exercise, we are multiplying the value of one dime by the total number of dimes Claire has.
For example, if Claire has 12 dimes (y = 12), then: \( 10 \times 12 = 120 \) cents.
Multiplication helps us find the total value quickly and efficiently.
Equation Formation
Equations are a way to represent mathematical relationships.
In this problem, we need to create an equation to express the total value of Claire's dimes.
If Claire has \( y \) dimes, we multiply \( y \) by the value of one dime (10 cents).
The resulting equation is: \[ 10y \]
This equation shows the total value of the dimes in terms of y.
Currency Conversion
Currency conversion involves changing a sum of money from one currency to another.
In this particular exercise, we converted the number of dimes Claire has into cents.
This is a form of currency conversion because we are expressing value in a different unit (from dimes to cents).
For example, if Claire has 3 dimes, converting it to cents involves multiplying the number of dimes by 10: \[ 3 \times 10 = 30 \] cents.
Understanding currency conversion is crucial for accurately determining the value of money in various forms.

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