Five times a number plus four times the same number is equal to 360. What is the number?
2 answers:
Answer:
The number is 40.
Step-by-step explanation:
Let the number be x.
Given the statement: Five times a number plus four times the same number is equal to 360.
"Five times a number" means 5x
"Four times the same number" means 4x
Then, as per the given information we have;
Combine like terms;
9x = 360
Divide both sides by 9 we get;
x = 40
Therefore, the number is, 40.
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We can replace the variables in this equation with the values from the points we have been given, (
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.
Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as
and we can change the improper fraction in the numerator into a mixed number for ease of addition.
And here, we can add, since it's made simple for us.
Finally, to get the slope we can complete the fraction by dividing.
The slope of this equation,
Now, to find y-intercept.
To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.
Let us substitute in our values.
Now, we can solve by multiplying the 7 and 2.
Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with
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Now, we can make this known in our equation like this:
Or, for neatness' sake, we can just say
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