Answer:
x cubed minus y cubed is equal to 504
Step-by-step explanation:
First we need to know what the values of x and y are. We can do this pretty easily, by just solving both equations for x, and equating them to each other:
With the first:
x + y = 10
x = 10 - y
And with the other
x - y = 6
x = 6 + y
Now that we have two definitions of x, we can say that the expressions are equal, and solve for y:
10 - y = 6 + y
10 - 6 = y + y
4 = 2y
y = 2
And now that we know what y is, we can find x:
x = 10 - y
x = 10 - 2
x = 8
So x is equal to eight. We can check our answer by plugging x into the other equation and seeing if we get the same value for y:
x - y = 6
8 - y = 6
-y = 6 - 8
-y = -2
y = 2
So we know we solved that correctly.
Now if we cube each number, eight cubed is equal to 512, and 2 cubed is equal to 8. If we subtract the latter from the former we get 504.
so x cubed minus y cubed is equal to 504
Average time of a commuter train trip from one town to the city = 77 minutes
Time taken by 1 trip = 71 minutes
Time taken by another trip = 74 minutes
Time taken by 3rd and 4th trip each = 78 minutes
Let us assume the time taken during the 5th trip = x
Then
(71 + 74 + 78 +78 +x)/5 = 77
301 + x = 77 * 5
301 + x = 385
x = 385 - 301
= 84 minutes
So the length of the fifth trip was 84 minutes. I hope the procedure is clear enough for you to understand.
The answer is numbers 2 and 3
Salary = $ 30,000
10% of salary =
= $ 3,000
Hence, 10% increase in the salary
= 30,000 + 3,000 = $ 33,000
Thus, the answer is $ 33,000.
Answer:
31 and 28
Step-by-step explanation:
<u>Let x represent the first number.</u>
<u>Let y represent the second number.</u>
x + y = 59
x - y = 3
<u>Use substitution method to solve.</u>
x = y + 3
y + 3 + y = 59
2y + 3 = 59
<u>Subtract both sides by 3.</u>
2y = 56
<u>Divide both sides by 2.</u>
y = 28
<u>Let's find the second number.</u>
59 - 28 = 31
<u>Check</u>
31 -28 = 3
<u>Answer</u> The two numbers are 28 and 31.
