Question

Rita makes and sells necklaces. The materials to make each necklace cost $2. 75. Last week she made 8 necklaces and wants to make a total profit of $78. Using the equation 8 (x 2. 75) = 78, Rita determined that she needs to sell each necklace for $7 to make a total profit of $78. Which error did Rita make? Although she has the correct equation, she needs to sell each necklace for $12. 50. Although she has the correct solution, she should have used the equation 8 (x minus 2. 75) = 78. The equation should be 8 (x minus 2. 75) = 78, and she needs to sell each necklace for $12. 50. The equation should be StartFraction 1 over 8 EndFraction (x minus 2. 75) = 78, and she needs to sell each necklace for $75. 25.

Answer 1

Profit function gives the profit earned for given input. Thus, Rita has correct solution, that is, she needs to make 7 necklace to get $78 profit.

How to find the value of unknown variable in a linear equation?

It might not be always possible. But for simple cases, we can try using addition or subtraction or such operations in linear equations if there is single variable with single equation.

For the given case, the profit $78 for x necklace manufactured is

$8(x + 2.75) = 78$

(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in $2 \times (x + 3) = 2(x + 3)$)

Solving this equation, we get:

$8(x + 2.75) = 78\\\\\text{Dividing by 8 on both the sides}\\\\(x + 2.75) = \dfrac{78}{8} = 9.75\\\\\text{Subtracting 2.75 from both the sides}\\\\x = 9.75 - 2.75 = 7$

Rita has correct solution, that is, she needs to make 7 necklace to get $78 profit.

Learn more about solving linear equations here:

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