SOLUTION: I am helping my little sister with her math homework. The word problem is: There are 18 bikes in a bike rack. There are 4 more blue bikes than yellow bikes, and 2 less yellow bik

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Question 560887: I am helping my little sister with her math homework. The word problem is: 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? I figured out the answer by guessing and verifying with quick math(8 blue, 4 yellow and 6 green) but she needs to show how she arrived at those numbers. I know it's an equation but have been unable to figure it out. I'm sure it's so simple. Would appreciate your help on this. Thanks!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let b = no. of blue bikes
let y = no. of yellow
let g = no. of green
:
Write an equation for each statement:
:
"There are 18 bikes in a bike rack."
b + y + g = 18
:
" There are 4 more blue bikes than yellow bikes,"
b = y + 4
:
"and 2 less yellow bikes than green bikes."
y = g - 2
We want to get g in terms of y also
add 2 to both sides
g = y + 2
:
In the 1st equation: replace b with (y+4); replace g with (y+2)
b + y + g = 18
(y+4) + y + (y+2) = 18
Combine like terms
3y + 6 = 18
3y = 18 - 6
3y = 12
y = 12/3
y = 4 yellow bikes
then
b = y +4
b = 4 + 4
b = 8 blue bikes
and
g = y + 2
g = 4 + 2
g = 6 green bikes
:
Check this by seeing if they add up to 18
8 + 4 + 6 = 18