The day after the school election it was reported that Danny won the election for class president. For every three votes his opponent received, Danny received 5 votes. Every student voted exactly once. If the students voted only for either Danny or his opponent and Danny's opponent received 312 votes, how many students voted in the election?

832 votes were cast

Step-by-step explanation:

Danny received  =          5 of every 8 votes

Opponent received  =     3 of every 8 votes

Let V stand for the total number of votes cast.

The opponent's 3/8 of the votes was 312  so  (3/8) times V  = 312

(3/8)(V)  =  312

V  =  (312)/(3/8)              ( i.e., 312 divided by 3/8 )

To divide by a fraction, you invert the divisor and multiply

V  = (312) x (8/3)  =  2496/8  =  832 total votes  

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40