SOLUTION: Twenty-Five students will go to one the countries: Japan, Egypt, and Italy for six weeks during summer. The number of students going to Japan or Italy is five more than the number

Question 1111848: Twenty-Five students will go to one the countries: Japan, Egypt, and Italy for six weeks during summer. The number of students going to Japan or Italy is five more than the number of students going to Egypt. The number of students going to Japan is two less than the number going Egypt. How many students are going to each country?
Japan:
Egypt:
Italy:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let j = no. of students who go to Japan
let e = no. to Egypt
let I = no. to Italy
:
Write an equation for each statement
:
Twenty-Five students will go to one the countries: Japan, Egypt, and Italy
j + e + i = 25
:
The number of students going to Japan or Italy is five more than the number of students going to Egypt.
j + i = e + 5
j - e + i = 5
:
Use elimination with these two equation
j + e + i = 25
j - e + i = 5
------------------Subtraction eliminates j and i, find e
0 + 2e + 0 = 20
e = 20/2
e = 10 going to Egypt
:
The number of students going to Japan is two less than the number going Egypt.
j = e -2
replace e with 10
j = 10 - 2
j = 8 going to Japan
:
Find i using the 1st equation, replacing e and j
8 + 10 + i = 25
i = 25 - 18
i = 7 going to Italy
:
Check solutions in the statement
"The number of students going to Japan or Italy is five more than the number of students going to Egypt."
8 + 7 = 10 + 5
:
How many students are going to each country?
Japan: 8
Egypt: 10
Italy: 7
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