Q.8: If 84 monkeys are to climb 2016 ft in 2 hours, with each monkey climbing 1 ft in 5 minutes, what is the…

Question

Q.8: If 84 monkeys are to climb 2016 ft in 2 hours, with each monkey climbing 1 ft in 5 minutes, what is the correct option? Q.9: Round 7.887 to the nearest hundredth. Q.10: Let the two numbers be x a

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Here are the solutions to the questions:

Q.8

Determine the total time available.
The time available is from 8 pm to 10 pm, which is 2 hours.
$2 \text{ hours} = 2 \times 60 \text{ minutes} = 120 \text{ minutes}$
Calculate the height one monkey can climb in the available time.
The problem states that a monkey takes 5 minutes to climb "a wall". Assuming "a wall" refers to a unit of height, for example, 1 foot, then:
Rate of one monkey = $\frac{1 \text{ ft}}{5 \text{ min}}$
Height climbed by one monkey in 120 minutes = $\frac{1 \text{ ft}}{5 \text{ min}} \times 120 \text{ min} = 24 \text{ ft}$
Calculate the number of monkeys needed.
The total height to be climbed is 2016 ft.
Number of monkeys = $\frac{\text{Total height to climb}}{\text{Height climbed by one monkey in available time}}$
Number of monkeys = $\frac{2016 \text{ ft}}{24 \text{ ft/monkey}} = 84 \text{ monkeys}$

The correct option is (A).
$\boxed{\text{A) } 84}$
Q.9
To round 7.887 to the nearest hundredth, we look at the digit in the thousandths place.
The number is 7.887.
The hundredths digit is 8.
The digit to its right (in the thousandths place) is 7.
Since 7 is 5 or greater, we round up the hundredths digit.
Rounding 7.887 to the nearest hundredth gives 7.89.

The correct option is (B).
$\boxed{\text{B) } 7.89}$
Q.10
Set up the equations.
Let the two numbers be $x$ and $y$ .
"Twice the sum of two numbers is 484":
$2(x + y) = 484$ $x + y = \frac{484}{2}$ $x + y = 242 \quad (\text{Equation 1})$
"twice the difference is 52":
$2(x - y) = 52$ $x - y = \frac{52}{2}$ $x - y = 26 \quad (\text{Equation 2})$
Solve the system of equations.
Add Equation 1 and Equation 2:
$(x + y) + (x - y) = 242 + 26$ $2x = 268$ $x = \frac{268}{2}$ $x = 134$
Substitute $x = 134$ into Equation 1:
$134 + y = 242$ $y = 242 - 134$ $y = 108$
The two numbers are 134 and 108. The smaller number is 108.
Calculate the value of the smaller number divided by 2.
$\frac{108}{2} = 54$
The correct option is (D).

Q.8: If 84 monkeys are to climb 2016 ft in 2 hours, with each monkey climbing 1 ft in 5 minutes, what is the correct option? Q.9: Round 7.887 to the nearest hundredth. Q.10: Let the two numbers be x a

Answer

Step-by-step solution

Determine the total time available.

Calculate the height one monkey can climb in the available time.

Calculate the number of monkeys needed.

Set up the equations.

Solve the system of equations.

Calculate the value of the smaller number divided by 2.

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