find two numbers such that if 7 is added to the greater the answer is four times the smaller number, while 28 added to the smaller number is equal to twice the greater number.
4x = y+7
x+28 = 2y
The numbers are 6 and 17
Let's assume the two numbers as x and y.
Based on the given information, we can form two equations:
Equation 1: y + 7 = 4x
Equation 2: x + 28 = 2y
To solve this system of equations, we can use the substitution or elimination method. Let's solve it using the substitution method:
From Equation 2, we can rearrange it:
x = 2y - 28
Substitute this value of x into Equation 1:
y + 7 = 4(2y - 28)
Simplify the equation:
y + 7 = 8y - 112
7 + 112 = 8y - y
119 = 7y
Divide both sides by 7 to solve for y:
y = 17
Substitute the value of y back into Equation 2 to solve for x:
x + 28 = 2(17)
x + 28 = 34
x = 6
Therefore, the two numbers are x = 6 and y = 17.
To solve this problem, let's assign variables to the two numbers. Let's call the greater number "x" and the smaller number "y".
According to the problem, if 7 is added to the greater number, the result is four times the smaller number. This can be written as an equation: x + 7 = 4y.
Similarly, if 28 is added to the smaller number, the result is twice the greater number. This can be written as another equation: y + 28 = 2x.
Now we have a system of two equations with two variables:
Equation 1: x + 7 = 4y
Equation 2: y + 28 = 2x
To solve this system, we can use substitution or elimination method. Let's use substitution:
From Equation 1, we can rearrange it to solve for x: x = 4y - 7.
Now substitute this expression for x in Equation 2:
y + 28 = 2(4y - 7)
Simplify the equation:
y + 28 = 8y - 14
Combine like terms:
14 + 28 = 8y - y
42 = 7y
Divide both sides by 7:
y = 6
Now substitute the value of y back into Equation 1 or 2 to find the value of x. Let's use Equation 1:
x + 7 = 4(6)
x + 7 = 24
Subtract 7 from both sides:
x = 17
So the two numbers are x = 17 and y = 6.