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Calculate Electricity Bill Using Linear Formula c=14n+19 for 350 Units
Mathematics
Grade 7 (Junior High School)
Question Content
An electricity company uses the formula below to calculate bills. How much is Leah's bill if she uses 350 units of electricity? Formula: c = 14n + 19, where c = total cost in pence, n = number of units of electricity
Correct Answer
5019 pence
Detailed Solution Steps
1
Step 1: Identify the given values and variables. We know that n (number of electricity units) = 350, and the cost formula is c = 14n + 19.
2
Step 2: Substitute the value of n into the formula. Replace n with 350: c = 14*350 + 19.
3
Step 3: Calculate the multiplication first: 14*350 = 4900.
4
Step 4: Perform the addition to find the total cost: 4900 + 19 = 5019.
Knowledge Points Involved
1
Substitution into algebraic formulas
This refers to replacing variables in a formula with known numerical values to solve for an unknown quantity. It is a foundational skill in algebra, used to apply real-world formulas like cost, distance, or area calculations when specific values are given.
2
Order of operations (PEMDAS/BODMAS)
This rule dictates the sequence of calculations: Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division, and finally Addition and Subtraction. In this problem, we multiply 14 by 350 before adding 19 to follow this rule.
3
Real-world linear formula application
Linear formulas in the form y = mx + b are used to model relationships where one quantity increases at a constant rate relative to another. Here, 14n represents the variable cost per electricity unit, and 19 represents a fixed base cost, which is a common model for utility billing.
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