I am having a lot of trouble with story problems, especially creating the equations. Help please.
1. there are twice as many boys as girls in mrs. taylors class. When 3 new girls join her class, she will have 24 students. How many boys and girls were originally in her class?
2. The local cable television company offers two deals. Basic cable tv service with one movie channel costs $35 per month. Basic service with two movie channels costs $45 per month. Find the charge for the basic cable service and the charge for each movie channel.
3. With a tail wind, a plane traveled 800 mi. in 5 hrs. With a head wind, the plane traveled the same distance in 8 hrs. Find the plane's air speed and the speed of the wind. Assume they're both constant.
4. The units of a two-digit number are reversed is twice the tens digit. If the digits are reversed, the new number is 36 less than the original number. Find the original number.
Let speed of plane = x km/h
Let speed of wind = y km/h
Speed of plane with tail wind = (x + y) km/h
Speed of plane with head wind = (x - y) km/h
Distance travelled by plane with tail wind = speed . time
800 = (x + y)(5)
so, x + y = 160 ................(1)
Distance travelled by plane with head wind = speed . time
800 = (x - y)(8)
so, x - y = 100 ..................(2)
Solve these two equations, got it now???
Let unit's digit = x
ten's digit = y
Number = 10y + x
Reversed number = 10x + y
According to first condition, y = 2x ................(1)
Reversed number = original number - 36
10x + y = 10y + x - 36
Put the value of y in this equation from eqn(1)
10x + 2x = 10(2x) + x - 36
x = 4
y = 8
Number = 10(8) + 4 = 84