We will need to use the substitution method to solve the question. The difference between the two numbers is 11.5
Substitution method is used to solve a system of equations. First the equation is solved for one variable and then the value is used in the other equation to solve for the other unknown variable. In this question we have been told the sum of two numbers is 32. Let us take the two numbers as x and y. Then we can say that
x+y=32 ...(i)
Next we know that when 5 is subtracted from 4 times one number the result is 8 times the other number, we can write it as
4x-5=8y
4x-8y=5....(ii)
So we have two equations
x+y=32
4x-8y=5
We will multiply equation (i) by 4 to cancel out x and solve for y
4x+4y=128
4x-8y=5
(-) (+) (-)
-----------------
12y=123
y=10.25
We substitute the value of y in equation (i)
x+y=32
x+10.25=32
x=32-10.25=21.75
We need to find the difference between two number which is x-y=21.75-10.25=11.5
Therefore we found out by substitution method that the difference between the two numbers is 11.5
Learn more about substitution method here:
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