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?
Madelyn
4.782 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 c = 80
2. Multiply the first equation by 7 and the second equation by 5 to align the coefficients of \( p \):
3. Subtract the second equation from the first to eliminate \( p \):
4. Substitute \( c \) back into the first original equation to solve for \( p \):
Thus, the solution to the system is
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