An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Represent the unknown number with the variable c .
Express the product of 3 and the number as 3 c .
Subtract 9 from the product to represent 'Nine less than,' resulting in 3 c − 9 .
Set the expression equal to 4, forming the equation 3 c − 9 = 4 .
Explanation
Understanding the Sentence Structure Let's break down the sentence piece by piece to translate it into a mathematical equation. This will help us understand how each part of the sentence corresponds to a part of the equation.
Translating the Sentence The sentence states 'Nine less than the product of 3 and a number is equal to 4.'
'a number' is represented by the variable c .
'the product of 3 and a number' means 3 multiplied by c , which is 3 c .
'Nine less than the product of 3 and a number' means we subtract 9 from 3 c , resulting in 3 c − 9 .
'is equal to 4' means the expression 3 c − 9 is equal to 4, so we have 3 c − 9 = 4 .
The Final Equation Therefore, the equation that represents the sentence is: 3 c − 9 = 4
Examples
Imagine you're buying concert tickets. Each ticket costs $3, but you have a coupon that takes $9 off the total price. If you end up paying $4, this equation helps you figure out how many tickets you bought. The equation 3 c − 9 = 4 models this situation, where c is the number of tickets. Solving such equations is useful in many real-life scenarios, from calculating costs to determining quantities in various situations.
A device delivering a current of 15.0 A for 30 seconds moves approximately 2.81 × 10^{21} electrons. This is calculated using the relationship between current, charge, and the number of electrons. The total charge is 450 Coulombs, and dividing this by the charge of a single electron gives the total number of electrons.
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