Question 1121978: there were 48 entries from Grade 1 and Grade 2 in a storytelling competition. The rest were from Grade 3. If 30 entries were not from Grade 1 and 28 entries were not from Grade 2, how many entries were there altogether?
Found 3 solutions by Boreal, MathTherapy, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x=from Grade 1
y-from Grade 2
z=from Grade 3
x+y=48
y+z=30, z=30-y
x+z=28
therefore, x+30-y=28
and x+y=48
2x+30=76
2x=46
x=23
y=48
z=5
There were 76 entries altogether.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
there were 48 entries from Grade 1 and Grade 2 in a storytelling competition. The rest were from Grade 3. If 30 entries were not from Grade 1 and 28 entries were not from Grade 2, how many entries were there altogether?
Correct answer: 
Accept no other!!
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
x = from Grade 1
y - from Grade 2
z = from Grade 3
x+y = 48 (1) ("there were 48 entries from Grade 1 and Grade 2")
y+z = 30, (2) {"30 entries were not from Grade 1")
x+z = 28. (3) ("28 entries were not from Grade 2")
Add equations (1) and (2). You will get
x + 2y + z = 48 + 30 = 78. (4)
In equation (4), replace (x+z) by 28, based on eq(3). You will get
28 + 2y = 78 ====> 2y = 78-28 = 50 ====> y = 50/2 = 25.
Now from equation (1), x = 48-25 = 23.
From equation (2), z = 30-25 = 5.
Answer. x= 23; y= 25; z= 5. x + y + z = 23 + 25 + 5 = 53.
53 entries altogether.
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