Harry and Emily each have some sweets in their pockets.
If Harry gives Emily two sweets, she will have three times as many sweets as Harry.
If, on the other hand, Emily gives two sweets to Harry, then they will each have the same number of sweets.
How many sweets did they each start off with?
Answer:
The number of sweets Emily has is E and the number of sweets Harry has is H.
Now we can use this to put the scenarios into equations…
Scenario 1: E + 2 = 3(H – 2) Scenario 2: E – 2 = H + 2
We can simplify equation 2…
E – 2 = H + 2
E – 4 = H
Now we can substitute that into equation 1…
E + 2 = 3(E – 4 – 2)
E + 2 = 3(E – 6)
E + 2 = 3E – 18
2E = 20
E = 10
Now we can substitute our value for H into equation 2…
10 – 4 = H
H = 6
Therefore, Emily had 10 sweets and Harry had 6.