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