Let's call the two numbers 
and 
.
Given these variables, we can say: 
, based on the first sentence in the problem.
Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:
To solve, we can simply substitute 
in for in the second equation and solve.
- Get terms on the left side to a common denominator for easier addition
- Cross multiplication (
)
- Subtract
from both sides of the equation
- Factor left side of the equation
Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,
,
Since is not positive in this case, 
is not a solution.
Thus, 
is our only solution. In this case,
,
which means that the smaller number is 14 and the larger number is 28.
Answer:
15
Step-by-step explanation:
To get 10 percent, you divide by 10.
150 divided by 10 equals 15.
Answer:
(2,-1)
Step-by-step explanation:
The ys in both questions are isolated on one side of the equation in both. The numerical coefficient of both is 1. Therefore you should equate the the left side of each equation to the other left side. The solution is the easiest one to solve because there is only 1 unknown on both sides.
4x - 9 = x - 3 Subtract x from both sides.
4x-x - 9 = -3 Combine
3x -9 = - 3 Add 9 to both sides
3x - 9+9 = - 3+9
3x = 6 Divide by 3
3x/3 = 6/3
x = 2
===============
Now use the second equation to solve for y
y = x - 3
y = 2 - 3
y = -1
==============
The solution is (2,-1)
