Question 830508
THE FIFTH GRADER WAY:
Sally ended up with $12,
but before she got those $8 for washing the family car, she must have had
$12 - $8 = $4.
If she started with he whole weekly allowance,
after spending {{{1/2}}} of it,
she would have been left with the other {{{1/2}}} of her weekly allowance.
Apparently, that {{{1/2}}} of her weekly allowance was $4.
Then, her weekly allowance must be twice as much, meaning
2($4) = $8.
 
THE ALGEBRA WAY:
{{{x}}}= Sally's weekly allowance in $.
${{{(1/2)x}}}= what Sally spent going to the movies.
${{{x-(1/2)x}}}= what Sally had after going to the movies.
${{{x-(1/2)x+8}}}= what Sally had after going to the movies, washing the car, and getting paid for washing the car.
The problem says that equals $12, so our equation is
{{{x-(1/2)x+8=12}}}
 
Solving:
{{{x-(1/2)x+8}}}
We take out {{{x}}} as a common factor and get
{{{(1-1/2)x+8=12}}}
{{{(1/2)x+8=12}}}
We subtract {{{8}}} from both sides of the equal sign and get
{{{(1/2)x+8-8=12-8}}}
{{{(1/2)x=4}}}
We multiply both sides of the equal sign times {{{2}}}
(it is the same as dividing by {{{1/2}}} ) and get
{{{2*(1/2)x=2*4}}}
{{{highlight(x=8)}}}