Question 325233: Please solve these problems
Solve: 3(x − 1) − (x + 5) = 2
Mike is six less than three times his daughter's age. Mike is 36; how old is his daughter?
In a certain county, the number of Charter Schools is ten less than twice the number of Alternative Schools. We know that there are 46 Charter Schools in the county. How many Alternative Schools are in the county?
The formula for degrees Celsius is: C = (F − 32), where F stands for degrees Fahrenheit.
Part 1: Solve the formula for F. Show all steps.
Part 2: Determine how many degrees Fahrenheit 4 degrees Celsius is.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! First problem:
Solve: 3(x − 1) − (x + 5) = 2
Remove parentheses to get:
3x - 3 - x - 5 = 2
Combine like terms to get:
2x - 8 = 2
Add 8 to both sides of the equation to get:
2x = 10
Divide both sides of the equation by 2 to get:
x = 5
Substitute in original equation to get:
3(x-1) - (x+5) = 2 becomes:
3(5-1) - (5+5) = 2 becomes:
12 - 10 = 2 becomes:
2 = 2 which is true confirming that x = 5 is a good answer.
Second Problem:
Mike is six less than three times his daughter's age. Mike is 36; how old is his daughter?
Let m = mike's age and d = his daughter's age.
Formula you are looking for is:
m = 3*d - 6
What this says is that mike's age is 6 less than 3 times his daughter's age.
Since mike is 36, this formula becomes:
36 = 3*d - 6
Add 6 to both sides of this equation to get:
42 = 3*d
Divide both sides of this equation by 3 to get:
d = 14
Mike's daugher's age is 14.
Mike is 36
Multiply 14 by 3 to get 42.
Subtract 6 from 42 to get 36.
Equation is confirmed as correct.
Mike is 36.
His daughter is 14.
Third Problem:
In a certain county, the number of Charter Schools is ten less than twice the number of Alternative Schools. We know that there are 46 Charter Schools in the county. How many Alternative Schools are in the county?
Let c = the number of charter schools.
Let a = the number of alternative schools.
c = 2*a - 10.
Number of charter schools is 46.
This makes our equation equal to:
46 = 2*a - 10
Add 10 to both sides of this equation to get:
56 = 2*a
Divide both sides of this equation by 2 to get:
a = 28
There are 28 alternative schools in the country.
Multiply that by 2 to get 56.
Subtract 10 to get 46.
That's the number of charter schools in the country which is correct so the answer is good.
Fourth problem:
The formula for degrees Celsius is: C = (F − 32), where F stands for degrees Fahrenheit.
Part 1: Solve the formula for F. Show all steps.
Part 2: Determine how many degrees Fahrenheit 4 degrees Celsius is.
You start with C = (F-32).
Since this is not correct, you have a problem already.
The correct formula is:
C = (5/9) * (F - 32)
To solve this formula for F, do the following:
Multiply the formula out to get:
C = ((5/9) * F) - ((5/9) * 32))
Add ((5/9) * 32) to both sides of this equation to get:
C + ((5/9) * 32) = ((5/9) * F)
Multiply both sides of this equation by (9/5) to get:
((9/5) * C) + ((9/5) * (5/9) * 32) = F
The (9/5) * (5/9) cancels out and you are left with:
((9/5) * C) + 32 = F
You now have 2 formulas.
One formula for Fahrenheit and one formula for Celsius.
They are:
C = (5/9) * (F-32)
F = ((9/5) * F) - 32
To convert from one to the other, we'll take some known numbers.
32 degrees fahrenheit should equal 0 celsius.
We get:"
C = (5/9) * (32-32) = (5/9) * 0 = 0 so this is good.
212 degrees fahrenheit should equal 100 celsius.
C = (5/9) * (212-32) = (5/9) * 180 = 100 so this is good.
If we have 4 degrees celsius, then what is the fahrenheit?
We get:
F = (9/5) * 4 + 32 which becomes:
F = 36/5 + 32 which becomes:
F = 39.2 degrees.
To confirm, we work our way back to celsius from fahrenheit.
C = (5/9) * (39.2 - 32) = (5/9) * (7.2) = 4
We can go back and forth so the equations are good.
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