jane had $7 and her sister had $2. their parents gave 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
Dien
after the giving:
jane --- 7+x
sister --- 2+x
now jane has twice as much as her sister.
7+x = 2(2+x)
7+x = 4 + 2x
-x = -3
x=3
They each got $3.00
check:
jane now has 10
her sister has 5,
does Jane have twice as much as the sister ???
Not understanding x
Not understanding the meaning of ‘x’
To solve this problem, we need to use algebra. Let's assume that the amount of money given to each of them by their parents is 'x'.
According to the problem, Jane had $7 and her sister had $2 before their parents gave them money. After receiving money from their parents, Jane had twice as much money as her sister.
Based on this information, we can create two equations:
1. Jane's money after receiving money from her parents: $7 + x = 2(x)
2. Sister's money after receiving money from her parents: $2 + x = x
Now, let's solve the equations step by step:
1. Jane's money equation: $7 + x = 2(x)
Distribute 2 to x: $7 + x = 2x
Subtract x from both sides: $7 = 2x - x
Simplify: $7 = x
2. Sister's money equation: $2 + x = x
Subtract x from both sides: $2 = x - x
Simplify: $2 = 0
Since $2 = 0, it doesn't make sense in this context. Therefore, we ignore this equation.
The solution is x = $7. Hence, their parents gave each of them $7.