1)one number is four more than a second number. Twice the second is three more than the first. Find the numbers.
2)four times one number minus a second is 11, and the sum of the numbers is 14. Find the numbers.
let one number (the first ) be x
let the second number by y
Just translate the English into Math , after all Math is just a language
"one number is four more than a second number" ---> x = y+4
"Twice the second is three more than the first" ---> 2y = x+3
so lining them up
x - y = 4
x - 2y = -3
subtract:
y = 7
then from x = y+7
x = 11
The first number is 11, the second is 7
check:
is 11 four more than 7 ? YES
is twice 14 three more than 11 ? YES
I am right!!!
Try the second the same way, show me your work
To solve these problems, we can use a system of equations to represent the given information and find the values of the unknown numbers.
Let's start with the first problem:
1) Let's assume the first number is represented by 'x' and the second number by 'y'.
We are given that "one number is four more than a second number," which can be written as:
x = y + 4
We are also given that "twice the second is three more than the first," which can be written as:
2y = x + 3
Now we have a system of two equations:
x = y + 4
2y = x + 3
We can solve this system of equations using substitution or elimination method.
Let's choose the substitution method:
From the first equation, we see that x = y + 4. We can substitute this value of x into the second equation:
2y = (y + 4) + 3
2y = y + 7
Simplifying this equation, we get:
y = 7
Now substitute the value of y back into the first equation:
x = 7 + 4
x = 11
Therefore, the two numbers are x = 11 and y = 7.
Now let's move on to the second problem:
2) Let's assume the first number is represented by 'x' and the second number by 'y'.
We are given that "four times one number minus a second is 11," which can be written as:
4x - y = 11
We are also given that "the sum of the numbers is 14," which can be written as:
x + y = 14
Again, we have a system of two equations:
4x - y = 11
x + y = 14
Using the elimination method, we can add these two equations together to eliminate the variable 'y':
(4x - y) + (x + y) = 11 + 14
5x = 25
Dividing both sides of the equation by 5, we get:
x = 5
Now substitute the value of x back into the second equation:
5 + y = 14
y = 9
Therefore, the two numbers are x = 5 and y = 9.
By solving the system of equations for both problems, we have found the values of the unknown numbers.