Question

partially shown in the table.

	mornings	evenings
35 and older	17	( n )

65% (rounded) of the employees who prefer mornings are 35 and older.
40% of the employees who prefer evenings are 35 and older.

what is the value of ( m cdot n )?

enter your answer in the box.

( m cdot n = square )

Explanation:

Step1: Find m using the morning preference percentage

The number of employees who prefer mornings is \( m + 17 \). 65% of them are 35 and older, so \( 0.65(m + 17)=17 \). Solving for \( m \):
\( 0.65m + 11.05 = 17 \)
\( 0.65m = 17 - 11.05 = 5.95 \)
\( m=\frac{5.95}{0.65}=9.15\approx9 \) (since \( m \) should be a whole number, and checking \( 0.65(9 + 17)=0.65\times26 = 16.9\approx17 \), which matches)

Step2: Find n using the evening preference percentage

The number of employees who prefer evenings is \( 12 + n \). 40% of them are 35 and older, so \( 0.4(12 + n)=n \). Solving for \( n \):
\( 4.8 + 0.4n = n \)
\( 4.8 = n - 0.4n = 0.6n \)
\( n=\frac{4.8}{0.6}=8 \)

Step3: Calculate \( m\cdot n \)

Now that \( m = 9 \) and \( n = 8 \), we find \( m\cdot n=9\times8 = 72 \)

Answer:

72