Question

.- In a department store they put on sale shirts and pants that are out of season. On the first day, five pants and seven shirts were sold, for a total of $1,060. On the second day of sales, the amounts were reversed and $1,100 was earned. What was the price of a pair of pants and a shirt?

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Answer to a math question .- In a department store they put on sale shirts and pants that are out of season. On the first day, five pants and seven shirts were sold, for a total of $1,060. On the second day of sales, the amounts were reversed and $1,100 was earned. What was the price of a pair of pants and a shirt?

$Expert avatar$

Madelyn

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86 Answers

1. Write down the system of equations:

\begin{cases}5p + 7c = 1060 \\7p + 5c = 1100\end{cases}

2. Multiply the first equation by 7 and the second equation by 5 to align the coefficients of $ p $:

\begin{cases} 7(5p + 7c) = 7(1060) \\ 5(7p + 5c) = 5(1100) \end{cases}

\begin{cases} 35p + 49c = 7420 \\ 35p + 25c = 5500 \end{cases}

3. Subtract the second equation from the first to eliminate $ p $:

(35p + 49c) - (35p + 25c) = 7420 - 5500

24c = 1920

c = \frac{1920}{24}

c = 80

4. Substitute $ c $ back into the first original equation to solve for $ p $:

5p + 7(80) = 1060

5p + 560 = 1060

5p = 1060 - 560

5p = 500

p = \frac{500}{5}

p = 100

Thus, the solution to the system is

p = 100

and

c = 80

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