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Chapter 1: Problem 76

Write an original word problem that can be solved using a linear equation. Then solve the problem.

Short Answer

Expert verified
John sold approximately 13 bottles of lemonade to earn $30.

Step by step solution

01

Create the Word Problem

Here is an example of a possible word problem: 'John has started a lemonade stand. He pays $5 daily to rent the stand and $2 for each bottle of lemonade he sells. If he earns $30 in a day, how many bottles of lemonade did he sell?' In this scenario, the money John makes is directly dependent on the number of bottles he sells. This condition makes it a linear equation problem as there is a clear constant to how much he earns per bottle sold ($2), and he has a fixed cost ($5).
02

Translate to Linear Equation

In this problem, the number of bottles of lemonade that John sells can be represented by x. The cost for each bottle sold ($2) and the stand rent ($5) are constants. So, John's daily earnings which is equal to $30 can therefore be written as a linear equation: \(2x + 5 = 30\). This equation represents the relationship between John's earnings and the number of lemonade bottles he sells.
03

Solve the Linear Equation

To solve for x (number of bottles of lemonade sold), we need to isolate x on one side of the equation. We start by subtracting 5 from both sides to eliminate the +5 on the left side, and we get: \(2x = 30 - 5\) which simplifies to: \(2x = 25\). Then we divide each side of the equation by 2 to solve for x, and we get: \(x = 25 / 2\), which simplifies to \(x = 12.5\).
04

Interpret the Answer

The solution \(x = 12.5\) represents the number of bottles of lemonade that John sold to earn $30. However, in the context of the problem, it is not possible to sell half a bottle of lemonade. Thus, we will consider this as approximately 13, rounding upward to the nearest whole number (since selling 12 bottles would not achieve an income of $30). So, John sold about 13 bottles of lemonade to earn $30.

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Most popular questions from this chapter

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