The sum of two numbers is 28 the sum of 5 times the larger and 8 times the smaller is 161 find the numbers
Let's assume that the larger number is represented by "x" and the smaller number is represented by "y".
According to the statement, the sum of two numbers is 28:
x + y = 28 (Equation 1)
The sum of 5 times the larger number and 8 times the smaller number is 161:
5x + 8y = 161 (Equation 2)
We can solve this system of equations by substitution or elimination method.
Using the substitution method:
From Equation 1, we can express x in terms of y:
x = 28 - y
Now substitute this value of x in Equation 2:
5(28 - y) + 8y = 161
140 - 5y + 8y = 161
3y = 21
y = 7
Substitute the value of y in Equation 1:
x + 7 = 28
x = 28 - 7
x = 21
Therefore, the larger number is 21 and the smaller number is 7.