Variables on Both Sides
8t+5=6t+1
t = -2
10b+18=1/2(16b+8)
b = -7
9a = 6(a+4)
a = 8
The membership fee for joining a camping association is $45. A local campground charges members of the camping association $35 per night for a campsite and non-members $40 per night for a campsite. After how many nights of camping is the total cost for members, including the membership fee, the same as the total cost for nonmembers?
6 nights
8c+5=4c-11
c = -4
5(n+2)=3/5(5+10n)
n = 7
5h-7=2(h+1)
h = 3
Dan and Sydney are getting high-speed internet access at the same time. Dan's provider charges $60 for installation and $42.95 per month. Sydney's provider has free installation and charges $57.95 per month. After how many months will Dan and Sydney have paid the same amount for high-speed Internet service?
4 months
3x-4=2x+8-5x
x = 2
2(3g+2)=1/2(12g+8)
All real numbers, identity
2-15n=5(-3n+2)
2!=10
No solution
A rock-climbing gym offers a yearly membership for $360 where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for the equipment rental. After how many visits will the cost for a member and a non-member be the same?
30 visits
-15c+7c+1=3-8c
1!=3
No solution
3/4a=1/4(2a+8)
a = 8
3(d+12)=8-4d
d = -4
Currently you have $109 and your brother has $181. You decide to save $5 per week, while your brother spends his whole allowance plus $7 each week. How long will it be before you have as much money as your brother?
6 weeks
8w-8-6w=4w-7
w = -1/2
3/2+3/4a=1/4a-1/2
a = -4
5(1+4m)=2(3+10m)
5!=6
No solution
Central High's enrollment decreases at an average rate of 15 students per year, while Washington High's enrollment increases at an average rate of 35 students per year. Central High has 2166 students and Washington High has 1866 students. If enrollments continue to change at the same rate, when will the two schools have the same number of students?
6 years