Answer:
95
Step-by-step explanation:
Let x represent the ones digit. The tens digit will be higher, because reversing the digits results in a lower number. Its value is (14 -x). The given relation is ...
(10(14-x) +x) -(10x +(14 -x)) = 36 . . . . reversing the digits gives 36 less
140 -9x -9x -14 = 36 . . . . eliminate parentheses
90 = 18x . . . . . . . . add 18x-36
5 = x . . . . . . ones digit
14-5 = 9 . . . tens digit
The original number is 95.
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<em>Check</em>
95 -59 = 36
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<em>Additional comment</em>
The difference in value when the digits of a 2-digit number are reversed is always 9 times the difference in the digits. This means the difference in the digits is 36/9 = 4. Since the sum of digits is 14, the two digits are (14+4)/2 = 9 and (14-4)/2 = 5. 95 is the number of interest.
The solutions to a "sum and difference" problem are half the sum and half the difference of the given sum and difference. That is how we know the larger digit is (1/2)(14 + 4), for example.
We worked this "the hard way" using the above equation. It can actually be worked in your head if you're familiar with these generic solutions.
Answer:
Step-by-step explanation:
Given
per square yard
Required
Determine the cost of carpet and installation
First, calculate the area of the carpet
Convert to square yard
The cost is then calculated as:
Together they equal 90 degrees.
Equation:
(0.1x - 22) + (0.3x - 54) = 90
Open parenthesis and simplify:
0.4x -76 = 90
0.4x = 166
DIvide:
Your final answer is x= 415
Hope this helps!
Well, you can put various math problems into one. Equations can also show more information easier than writing many problems. Hope this helps, and keep learning!
