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There are 134 pots and pans.
(3)/(4) of the pots and
(2)/(5) of the pans are old. There are 74 old pots and pans. How many pots are there?

There are $134$ pots and pans. $\frac{3}{4}$ of the pots and $\frac{2}{5}$ of the pans are old. There are $74$ old pots and pans. How many pots are there?

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Mean, median, mode, and range: find the missing number

Full solution

Q. There are

134

pots and pans.

\frac{3}{4}

of the pots and

\frac{2}{5}

of the pans are old. There are

74

old pots and pans. How many pots are there?

Define Variables: Let's call the number of pots $P$ and the number of pans $N$ . We know that $P + N = 134$ .
Calculate Old Pots: We are told that $(\frac{3}{4})$ of the pots are old, which means $0.75 \times P$ are old pots.
Calculate Old Pans: We are also told that $\frac{2}{5}$ of the pans are old, which means $0.4 \times N$ are old pans.
Total Old Pots and Pans: The total number of old pots and pans is $74$ , so we can write the equation: $0.75 \times P + 0.4 \times N = 74$ .
Express $N$ in Terms of $P$ : We know that $P + N = 134$ , so we can express $N$ as $N = 134 - P$ .
Substitute N: Substitute $N$ in the old pots and pans equation: $0.75 \times P + 0.4 \times (134 - P) = 74$ .
Solve for P: Now, let's solve for $P$ : $0.75 \times P + 53.6 - 0.4 \times P = 74$ .
Combine Like Terms: Combine like terms: $0.35 \times P + 53.6 = 74$ .
Subtract $53$ . $6$ : Subtract $53.6$ from both sides: $0.35 \times P = 74 - 53.6$ .
Calculate Difference: Calculate the difference: $0.35 \times P = 20.4$ .
Divide to Find P: Divide both sides by $0.35$ to find $P$ : $P = \frac{20.4}{0.35}$ .
Perform Division: Perform the division: $P = 58.2857142857$ .

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