Annie want to buy a toy, but she has no money? If she saves for 3 weeks she will be $1 short of what it cost to buy the toy, if she saves for 4 weeks she will be $3 above the toy cost. How much is Annie saving every week? what is the cost of the toy?

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Answer 1 · 2016-09-24T14:18:12

She gets $4 a week, the toy costs $13.

The price of the toy represented by #y#.
The amount of money she gets per week is #x#.

#3x + 1 = y# (3 weeks is $1 short)
#4x - 3 = y# (4 weeks is $3 extra)

Therefore

# 3x + 1 = 4x - 3#

Then we take #3x# from both sides

#1 = x - 3#

Finally we add #3# to both sides

# 4 = x#

Her weekly allowance is, therefore, $4.

Then we can substitute in the value of #x# into an earlier equation to find #y#

#3x + 1 = y#
#3(4) + 1 = y#

#12+1 = y#
#13=y#

The toy, therefore, costs $13