The answer is 7
7^ ⁴ = 49
In a four-digit number, the first digit cannot be 0, so there are only 4 even numbers available. For the second, third, and fourth digits, there are 5 available numbers. Thus, the number of 4-digit numbers containing only even digits is 4 x 5 x 5 x 5 = 500 numbers.
You answered correctly for part a. just simplify it. so for part a it would be x^4 + 8x^3 + 24x^2 + 32x + 16. repeat what you did in part a with part b (add & simplify). btw, the missing side in part c is 2x-x = x
<span>let x = the original no. of students
then
(x+10) = the actual no. that went on the trip
:
= the original cost per student
and
= the actual cost
:
Original cost - actual cost = $12.50
- = 12.50
multiply equation by x(x+10)
x(x+10)* - x(x+10)* = 12.50x(x+10)
Cancel the denominators
1500(x+10) - 1500x = 12.5x(x+10)
1500x + 15000 - 1500x = 12.5x^2 + 125x
Combine on the right to form a quadratic equation
0 = 12.5x^2 + 125x - 15000
Simplify, divide equation by 12.5
x^2 + 10x - 1200 = 0
You can use the quadratic formula; a=1; b=10; c=-1200, but this will factor to
(x + 40(x - 30) = 0
The positive solution is what we want here
x = 30 students in the original group
Check this by finding the cost per student for each scenario
1500/30 = $50.00; original cost
1500/40 = $37.50; actual cost
---------------------
saving: $12.50</span>
