Solve each equation using simplification techniques. Round answers to two decimal places as necessary.
$-96=7(-17-2 C)$
Answer (2)
Distribute the 7 on the right side: − 96 = − 119 − 14 C .
Add 119 to both sides: 23 = − 14 C .
Divide by -14: C = − 14 23 .
Round to two decimal places: − 1.64 .
Explanation
Understanding the Problem We are given the equation − 96 = 7 ( − 17 − 2 C ) and asked to solve for C , rounding to two decimal places as necessary. Our goal is to isolate C by using simplification techniques.
Distributing First, distribute the 7 on the right side of the equation: − 96 = 7 ( − 17 ) + 7 ( − 2 C )
Simplifying Simplify the right side of the equation: − 96 = − 119 − 14 C
Isolating the Term with C Add 119 to both sides of the equation to isolate the term with C : − 96 + 119 = − 119 − 14 C + 119
Simplifying Simplify both sides of the equation: 23 = − 14 C
Solving for C Divide both sides of the equation by − 14 to solve for C : − 14 23 = − 14 − 14 C
Simplifying Simplify to solve for C : C = − 14 23
Rounding to Two Decimal Places Convert the fraction to a decimal and round to two decimal places: C ≈ − 1.64
Examples
Imagine you're buying concert tickets online. The total cost is $96, which includes a fixed booking fee of $17 per ticket and a service charge of $2 per ticket. If you bought 7 tickets, this problem helps you calculate the service charge (C) added to each ticket. By solving the equation, you find out how much extra you're paying for each ticket beyond the base price. This kind of calculation is useful for budgeting and understanding the breakdown of costs in various transactions.
After distributing and isolating the variable, we solved the equation − 96 = 7 ( − 17 − 2 C ) for C , finding that C ≈ − 1.64 when rounded to two decimal places.
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