Michael Z. answered • 05/29/15
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Mike, Master of Math
x=smaller number
y=larger number
Using the information given in the problem, you can write the following two equations.
1. y=4x+6
2. x=1/5y
Plug in x=1/5y to find the value of y.
y = 4(1/5y)+6
y = 4/5y+6
1/5y=6
y=30
Using x=1/5y and knowing that y=30, you can calculate that x=6.
Now check your work using the original two equations we made.
1. y=4x+6... 30=4(6)+6
2. x=1/5y... 6=1/5(30).
The two numbers are 6 and 30.
Michael J.
We do the same process.
Let smaller number = x
Let larger number = y
Set two equations.
x = (2/9)y eq1
x - y = 35 eq2
Substitute eq1 into eq2. This will get eq1 in terms of y.
(2/9)y - y = 35
(-7/9)y = 35
y = 35(-9/7)
y = 5(-9)
y = -45
Substitute this value of y into eq1 to solve for x.
x = (2/9)(-45)
x = 2(-5)
x = -10
Now if we compare these numbers, we will find that x is greater than y. We need x to be smaller than y because of the variables we inputted. So eq2 must say
y - x = 35
Lets try this again by substituting the same eq1 into this eq2.
y - (2/9)y = 35
(7/9)y = 35
y = 35(9/7)
y = 5*9
y = 45
Substitute this value of y into eq1.
x = (2/9)(45)
x = 2*5
x = 10
10 is less than 45. Therefore, the smaller is 10. The larger number is 45.
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05/29/15
Kevin Z.
05/29/15