There are 18 bikes in a bike rack. There are 4 more blue bikes than yellow bikes and 2 less yellow bikes than green bikes. How many bikes of each color are in the rack?
4 yellow bikes
8 blue bikes
6 green bikes
4+8+6=18
can you post how you solved it...I can
solve it using algebra.. but can't figure it out otherwise!!!
Ehh I just knew
from the information above:
I blue = yellow + 4
II yellow = green - 2
OR yellow +2 = green
and we know that
III yellow + blue + green = 18
now insert upper expressions into the III equation:
yellow + (yellow +4) + (yellow +2) = 18
3 yellow + 6 = 18
--> yellow = 4
insert 4 into upper equation and you will get
blue= 4+4
green= 4+2
18 bikes in all. 4 more blue than yellow, 2 less yellow than green, how many green bikes are there?
To solve this problem, we need to set up a system of equations to represent the given information. Let's represent the number of yellow bikes as "y", the number of blue bikes as "b", and the number of green bikes as "g".
From the given information, we can establish three equations:
1. There are 18 bikes in total:
y + b + g = 18
2. There are 4 more blue bikes than yellow bikes:
b = y + 4
3. There are 2 less yellow bikes than green bikes:
y = g - 2
Now we have a system of three equations with three variables. Let's solve it.
First, substitute equation (3) into equation (2) to get rid of the "y" variable:
b = (g - 2) + 4
b = g + 2
Next, substitute equations (2) and (3) into equation (1):
(g - 2) + 2 + g + g = 18
Combine like terms:
3g = 18
Divide both sides by 3:
g = 6
Now that we know "g" represents the number of green bikes, we can substitute it back into equation (3) to find "y":
y = 6 - 2
y = 4
Finally, we can substitute "g = 6" into equation (2) to find "b":
b = 6 + 2
b = 8
Therefore, there are 4 yellow bikes, 8 blue bikes, and 6 green bikes in the bike rack.