the sum of two numbers is the same as four times the smaller number.if twice the larger is decreased by the smaller,the result is 30.find the numbers
let x be the smaller, and y the larger
x+y = 4x
2y - x = 30
solve the two equations.
I would take the first down to y = 3x and use substitution
From the first statement, x + y = 4x, or y = 3x, x being the smaller number.
From the second statement, 2y - x = 30.
Substitute the first into the second and you are on your way.
Let's assume the two numbers are x and y, where x is the smaller number and y is the larger number.
Based on the given information:
1. The sum of x and y is equal to four times the smaller number:
x + y = 4x
2. Twice the larger number (2y) decreased by the smaller number (x) is equal to 30:
2y - x = 30
To solve this system of equations, we can use substitution or elimination method.
Let's solve it using substitution:
From equation 1, we can express y in terms of x:
y = 4x - x
y = 3x
Substituting this value of y in equation 2:
2(3x) - x = 30
6x - x = 30
5x = 30
x = 6
Now, substitute the value of x back into equation 1 to find y:
6 + y = 4(6)
y + 6 = 24
y = 24 - 6
y = 18
Therefore, the numbers are x = 6 and y = 18.
To solve this problem, let's assume the smaller number as "x" and the larger number as "y".
We are given two conditions:
1. The sum of two numbers is the same as four times the smaller number:
x + y = 4x
2. Twice the larger number decreased by the smaller number is equal to 30:
2y - x = 30
We will now solve this system of equations using the substitution method:
1. Rearrange the first equation to solve for x:
y = 3x
2. Substitute the value of y from the second equation into the first equation:
x + 3x = 4x
4x = 4x
The value of x cancels out, indicating that x can be any value.
This means that there are infinitely many solutions to this system of equations. In other words, there are infinite pairs of numbers that satisfy the given conditions.