Amy, Ben, Carrie and David went on an Easter egg hunt.
They found red, purple, yellow and green colored eggs.
The number of purple eggs that they found was three more than the number of green eggs.
The number of red eggs was twice the number of green eggs.
The number of yellow eggs was two more than the number of red eggs.
Amy found as many eggs as Ben did.
Carrie found three eggs more than Amy did.
David found four eggs more than Ben did.
Carrie, whose favorite color is red, gathered only red colored eggs.
None of the other kids gathered red colored eggs.
Answer the following:
1) How many red eggs did they find?
2) How many purple eggs did they find?
3) How many yellow eggs did they find?
4) How many green eggs did they find?
5) How many eggs did Amy find?
6) How many eggs did Ben find?
7) How many eggs did Carrie find?
8) How many eggs did David find?
You must solve this problem using algebra:
Let G = number of green eggs
Let R = number of red eggs
Let P = number of purple eggs
Let Y = number of yellow eggs
Let A = number of eggs that Amy found
Let B = number of eggs that Ben found
Let C = number of eggs that Carrie found
Let D = number of eggs that David found
Then set up equations and solve, showing all work!
Solution to the Problem:
1) There were 10 red eggs.2) There were 8 purple eggs.
3) There were 12 yellow eggs.
4) There were 5 green eggs.
5) Amy found 7 eggs.
6) Ben found 7 eggs.
7) Carrie found 10 eggs.
8) David found 11 eggs.
Let G = number of green eggs
Let R = number of red eggs
Let P = number of purple eggs
Let Y = number of yellow eggs
Let A = number of eggs that Amy found
Let B = number of eggs that Ben found
Let C = number of eggs that Carrie found
Let D = number of eggs that David found
Then set up the equations:
P = G + 3
R = 2G
Y = R + 2
A = B
C = A + 3
D = B + 4
C = R
A + B + C + D = G + R + P + Y
That gives you eight equations with eight variables.
You can express all the variables in terms of G.
R = 2G
P = G + 3
Y = 2G + 2
C = 2G
A = 2G - 3
B = 2G - 3
D = 2G + 1
Substituting into the 8th equation, we get
8G - 5 = 6G + 5
Then 2G = 10
So G = 5
Then R = 10
P = 8
Y = 12
A = 7
B = 7
C = 10
D = 11.
Correctly solved by:
| 1. Ivy Joseph | Pune, Maharashtra, India |
| 2. Kimberly Howe | Vienna, Virginia |
| 3. Rob Miles | Northbrook, Illinois |
| 4. Kelly Stubblefield | Mobile, Alabama |