Algebra Help?

Question

(a) choose a variable and indicate what it represents, (b) set up an equation to represent the problem described, (c) solve the equation,

5. A bill from a limousine company was $510. This included $150 for the service and $80 for each hour of use. Find the number of hours that the limousine was used.

6. Last week on an algebra test, the highest grade was 9 points less than three times the lowest grade. The sum of the two grades was 135. Find the lowest and highest grades on the test.

7. Ike has some nickels and dimes amounting to $2.90. The number of dimes is 1 less than twice the number of nickels. How many coins of each kind does he have?

8. The difference of two numbers is 16. Three-fourths of the larger number is 14 larger than one-half of the smaller number. Find the numbers.

Solve the following problem using proportions.
9. Suppose that a car can travel 264 miles using 12 gallons of gasoline. How far will it go on 15gallons?

THANK YOU SO MUCH

Answer 1

#5:

x = the number of hours in use:

510 = 150 + 80 * x
80x = 360
x = 4.5 hours

#6:

x = lowest grade
y = highest grade

y = 3x - 9
x + y = 135

y = 135 - x
135 - x = 3x - 9
144 = 4x
x = 36
y = 99

#7:

x = number of dimes
y = number of nickles

x = 2y - 1
10x + 5y = 290

10(2y - 1) + 5y = 290
25y - 10 = 290
25y = 300
y = 12
x = 23

#8

x = the larger number
y = the smaller number

x - y = 16
3/4x = 1/2y + 14

3x = 2y + 56
3(y + 16) = 2y + 56
3y + 48 = 2y + 56
y = 8
x = 24

#9:

264 / 12 = x / 15
x = 330

Answer 2

5.
'h' for hours
80h + 150 = 510
80h = 510 - 150
80h = 360
h = 360 / 80 = 36/8
h = 4.5
h = 4.5 hours (4 hrs. 30 mins).

6.
'g' = lowest grade
g + (3g -9) = 135
g + 3g - 9 = 135
4g = 135 + 9
4g = 144
g = 144/4 = 36 - lowest grade
3g - 9 = 99 - the highest grade.

7.
NOT being an American I do not know the currency values of dimes and nickels so I cannot help.

8.
Let the two numbers be 'x' & 'y'
Then
x - y = 16 (The Difference)
3x/4 = y/2 + 14 (the ratios)
3x/4 - y/2 = 14
3x/4 - 2y/4 = 14
3x - 2y = 14 x 4 = 56
3x - 2y = 56
Resolve 'x' & 'y' simultaneously:-
3x - 2y = 56
x - y = 16
To eliminate 'y' multiply through by (-2). So!!!
3x - 2y = 56
-2x+2y = -32 and subtract
_________
x = 24
So substitute 24 for 'x' in either of the equ'ns.
24 - y = 16
y = 8
So the two numbers are 24 and 8.

9
'm' for miles
264/12 = m /15
By algebraic manipulation we have
m = 264 x 15 /12
m = 330 miles.

Hope this helps; sorry about No.7.

Answer 3

For increasing cubic binomials the final formulation is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D

Answer 4

What do you have so far? Where are stuck? Can you do at least part (a) or (b) for any of the questions?