A boy has a certain number of sweets. If he eats 16 a day, they will last him 2 days longer than if he eats 18 a day. How many sweets has he?
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first, name the "unknowns"
x = # of sweets
d = # of days it takes to eat all the sweets if he eats 18 each day
from those definitions, we can write the equation
x= 18d (this says if you eat 18 each day for "d" days, you get the total number of sweets)
If he eats 16 a day, they will last him 2 days longer
this means it will take d+2 days to eat all of the sweets, and we can write
now we use both of these equations:
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from those two equations we see 18d must equal 16(d+2):
18d = 16(d+2)
now solve for d. distribute the 16 on the right side:
18d= 16d + 32
now add -16d to both sides. we get
2d = 32
now we can find x. use either of the equations, for example