The difference between two numbers is 77. Five times the smaller is equal to 7 more than the larger. What are the numbers?
Ah, a mathematical challenge! Let's find the solution while keeping the mood light. Let's call the smaller number "x" and the larger number "y."
Firstly, we know that the difference between the two numbers is 77. So, we can write the equation as:
y - x = 77
Now, the problem states that five times the smaller number is equal to seven more than the larger number.
Translated into an equation, this would be:
5x = y + 7
To make things interesting, let's rearrange the first equation for some more fun:
y = x + 77
Now we can substitute this into the second equation:
5x = (x + 77) + 7
Simplifying further:
5x = x + 84
Subtracting x from both sides gives us:
4x = 84
Dividing by 4, my dear friend, we find:
x = 21
Plugging this value back into the first equation:
y = x + 77
y = 21 + 77
y = 98
So, my hilarious conclusion is that the numbers are 21 and 98. Ta-da!
To solve this problem, let's assign variables to the two numbers. Let's call the smaller number "x" and the larger number "y".
According to the given information, the difference between the two numbers is 77. This can be written as:
y - x = 77 (equation 1)
It is also given that five times the smaller number is equal to 7 more than the larger number:
5x = y + 7 (equation 2)
Now, we can solve this system of equations to find the values of x and y.
Let's rearrange equation 1 to solve for y:
y = x + 77 (equation 3)
Substitute equation 3 into equation 2:
5x = x + 77 + 7
Simplify and solve for x:
5x - x = 84
4x = 84
x = 84/4
x = 21
Now, substitute the value of x back into equation 3 to solve for y:
y = 21 + 77
y = 98
Therefore, the smaller number is 21 and the larger number is 98.
To solve this problem, we need to set up an equation based on the information given.
Let's assume that the smaller number is represented by the variable "x" and the larger number by the variable "y."
The problem states that the difference between the two numbers is 77, so we can write the equation: y - x = 77.
The problem also states that five times the smaller number is equal to 7 more than the larger number, so we can write the equation: 5x = y + 7.
Now we have a system of two equations:
1) y - x = 77
2) 5x = y + 7
To solve this system of equations, we can use the substitution method or the elimination method.
Let's use the substitution method. We can rearrange equation (1) to solve for y: y = x + 77.
Now we substitute this expression for y in equation (2): 5x = (x + 77) + 7.
Simplifying the equation: 5x = x + 84.
To isolate x, we can subtract x from both sides: 5x - x = 84.
Simplifying further: 4x = 84.
Dividing both sides by 4, we find: x = 21.
Now that we know the value of x, we can substitute it back into equation (1) to find y: y - 21 = 77.
Add 21 to both sides: y = 77 + 21.
Simplifying: y = 98.
So, the solution to this problem is that the smaller number is 21, and the larger number is 98.
smaller ---- x
larger ----- x+77
5x = x+77 + 7
4x = 84
x = 21
smaller is 21 , larger is 98
check:
is their difference equal to 77? yes
5 times the smaller --> 105
7 more than the larger -- 98+7 or 105
all is good!