|
Question 1093260: 1.) If 15 cm on a map represents 2.5 km of actual ground, how many centimetres would 15 km of actual ground be on the map?
2.) If the ratio of yellow pigment to blue pigment in a shade of green paint is 2:3, how many drops of yellow pigment will be needed of 12 drops of blue are used?
3.) If this treatment costs the consumer $68.00 and the cost of labour and materials used is $14.20, what is the ratio of consumer price to actual cost?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! problem 1:
If 15 cm on a map represents 2.5 km of actual ground, how many centimetres would 15 km of actual ground be on the map?
15 cm on the map equals 2.5 km on the ground.
the ratio of m/g = 15 / 2.5
when g = 15 km, you want to find m.
your equation is 15 / 2.5 = x / 15
cross multiply to get 15 * 15 = 2.5 * x
divide both sides of this equation by 2.5 and solve for x to get:
x = 15 * 15 / 2.5 = 90
you can also do the following.
ratio of map to ground is 15 / 2.5
divide 15 by 2.5 to get m/g = 6
you get 6 cm on the map for every km on the ground.
15 km on the ground is therefore equal to 15 * 6 = 90 cm on the map.
------------------------
problem 2:
If the ratio of yellow pigment to blue pigment in a shade of green paint is 2:3, how many drops of yellow pigment will be needed of 12 drops of blue are used?
y = yellow
b = blue
y/b = 2/3 for a particular shade of green.
if 12 drops of blue, how many yellow are needed?
y/b = 2/3 = x/12
cross multiply to get 2*12 = 3*x
divide both sides of the equation by 3 and solve for x to get:
x = 2*12/3 = 2*4 = 8
you will need 8 drops of yellow if you have 12 drops of blue.
also you can do:
y/b = 2/3
solve for y to get y = 2/3 * b
when b = 12, then y = 2/3 * 12 = 2 * 4 = 8
--------------
problem 3:
If this treatment costs the consumer $68.00 and the cost of lab0r and materials used is $14.20, what is the ratio of consumer price to actual cost?
r = revenue equals consumer price = cost to the consumer
c = actual cost equals cost of labor and materials.
ratio of consumer price to actual cost would then be r/c
r = 68
c = 14.2
r/c = 68/14.2
that's the ratio.
solve for r to get r = 68/14.2 * c = 4.788732394 * c
solve for c to get c = r / (68/14.2) which becomes c = r * (14.2/68) which becomes c = .2088234294 * r
so, when r = 68, then c = .2088234294 * 68 = 14.2 and when c = 14.2, r = 4.788732394 * 14.2 = 68.
|
|
|
| |
