Question 687127: 1. April Day, Peter Rabbit, and Marsha Mallow all joined the Annual Easter Egg Hunt at the local park. When the hunt was over, the three friends sat down together and counted their eggs. April and Peter had a combined total of 25 eggs. Peter and Marsha had a combined total of 23 eggs. April and Marsha had a combined total of 24 eggs. How many eggs did each child find?
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! To solve this word problem, we need it turned into some equations.
We know what April and Peter had a combined total of 25 eggs. In equation form, this would be: A + P = 25, where A is April and P is Peter.
We know that Peter and Marsha had a combined total of 23 eggs. In equation form, this would be: P + M = 23, where P is Peter and M is Marsha.
We know that April and Marsha had a combined total of 24 eggs. In equation form, this would be: A + M = 24, where A is April and M is Marsha.
We now have 3 equations:
A + P = 25
P + M = 23
A + M = 24
In order to solve, let's first put the first equation in terms of P. To do this, subtract A from both sides, which gives us P = 25 - A
In the second equation, replace P with what P equals in the first equation. This gives us: 25 - A + M = 23. Now let's put this equation in terms of M. To do this, subtract 25 from both sides, and also add A to both sides, which will give us: M = 23 - 25 + A, which breaks down to M = A - 2.
Now, in the third equation, replace M with what M equals in our second equation. This gives us: A + A - 2 = 24. This breaks down to 2A - 2 = 24. We need to solve for A, so we will add 2 to both sides of the equal sign, giving us 2A = 24 + 2, which breaks down to 2A = 26. Divide both sides of the equal sign by 2 to give us A: A = 13.
We now know that April has 13 eggs.
If we go back to our first equation, A + P = 25, we can replace the A with 13: 13 + P = 25. Subtracting 13 from both sides, will give us P: P = 12.
We now know that Peter has 12 eggs.
Let's go back to the second equation, P + M = 23, and replace the P with 12: 12 + M = 23. Subtracting 12 from both sides, will give us M: M = 11
Marsha has 11 eggs.
Final Answer: April has 13 eggs, Peter has 12 eggs, and Marsha has 11 eggs
|
|
|
