Jane has $7 and her sister had $2. their parents have each of them an equal amount of money. then, jane had twice as much money as her sister. how much money did their parents give each of them?

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  $3

Step-by-step explanation:

The difference in the amounts doesn't change when each girl is given the same gift. That difference is $5. If Jane ends up with twice the amount her sister has, and that is $5 more, then Jane ends up with $10 and her sister ends up with $5.

$3 was given to each girl.

If x is the amount given to each girl, the equation can be ...

  (x+7)/(x+2) = (2)/(1)

  x +7 = 2x +4 . . . . multiply by (x+2)

  3 = x . . . . . . . . subtract x+4

  $3 was given to each girl.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is