Split 84 into 2 parts so that one part is five times the other part. What are both numbers?
Let's represent the two parts as x and 5x.
According to the problem, x + 5x = 84.
Combining like terms, we have 6x = 84.
To isolate x, we divide both sides of the equation by 6: x = 84/6 = 14.
Therefore, the two numbers are 14 and 5(14) = 70.
Find two numbers with a sum of 65. Twice the lesser number is 10 more than the greater number
Let's represent the two numbers as x and y.
According to the problem, we have the following equations:
x + y = 65 ...(1)
2x = y + 10 ...(2)
To solve the system of equations, we can substitute the value of y from equation (2) into equation (1):
x + (2x - 10) = 65
3x - 10 = 65
Adding 10 to both sides:
3x = 75
Dividing both sides by 3:
x = 25
Substituting x = 25 into equation (1):
25 + y = 65
Subtracting 25 from both sides:
y = 40
Therefore, the two numbers are 25 and 40.
E=mc squared. Solve.
The equation E=mc^2 is Einstein's famous equation from the theory of relativity, where E represents energy, m represents mass, and c represents the speed of light.
Solving this equation involves finding the value of E, given the values of m and c.
Let's say we have a mass value of m = 2 kg and the speed of light value c = 3 x 10^8 m/s.
To solve for E, we can simply substitute the given values into the equation:
E = (2 kg) * (3 x 10^8 m/s)^2
First, let's square the speed of light:
E = (2 kg) * (9 x 10^16 m^2/s^2)
Then, multiply the mass by the squared value:
E = 18 x 10^16 kg * m^2/s^2
Finally, we can simplify the expression:
E = 1.8 x 10^17 kg * m^2/s^2
The final result, E = 1.8 x 10^17 Joules.
235 people are at RSM summer camp. There are 35 more boys than girls and 70 fewer adults than girls. How many people from each group are there?
Let's represent the number of girls as x.
According to the problem, the number of boys is 35 more than the number of girls: boys = x + 35.
The number of adults is 70 fewer than the number of girls: adults = x - 70.
The total number of people is the sum of girls, boys, and adults, which is given as 235:
x + (x + 35) + (x - 70) = 235.
Now we can solve this equation for x:
3x - 35 = 235.
Adding 35 to both sides:
3x = 270.
Dividing both sides by 3:
x = 90.
So there are 90 girls.
The number of boys is x + 35 = 90 + 35 = 125.
The number of adults is x - 70 = 90 - 70 = 20.
Therefore, there are 90 girls, 125 boys, and 20 adults.
Kevin is six years older than Tim. 4 years ago, Kevin was twice as old as Tim. Find their present ages.
Let's represent Tim's present age as x years.
According to the problem, Kevin is six years older than Tim, so Kevin's present age is x + 6 years.
Four years ago, Tim's age was x - 4, and Kevin's age was (x + 6) - 4 = x + 2.
According to the problem, four years ago, Kevin was twice as old as Tim. So we can set up the equation:
x + 2 = 2(x - 4).
Expanding and simplifying the equation:
x + 2 = 2x - 8.
Subtracting x from both sides:
2 = x - 8.
Adding 8 to both sides:
10 = x.
Therefore, Tim's present age is 10 years.
Plugging this value into Kevin's present age equation, Kevin's present age is x + 6 = 10 + 6 = 16 years.
So, Tim is 10 years old and Kevin is 16 years old.