Ann has $198 more than her sister. After her mom gives Ann $20 and her sister $60, Ann has twice as much money as her sister. How much money did Ann have at first?

Question

Ann has $198 more than her sister. After her mom gives Ann $20 and her sister $60, Ann has twice as much money as her sister. How much money did Ann have at first?

Answer 1

Ann = a

Sister =s
a = s + 198
a+20 =2(s+60)

Substitute
s + 198 +20 = 2s + 120
s + 218 = 2s +120
218-120= 2s -s
s = 98
Ann got $296

Answer 2

To solve this problem, let's break it down step by step.

Let's assume the amount of money Ann's sister has as "x" dollars.
According to the given information, Ann has $198 more than her sister, so Ann's amount of money can be represented as "x + $198".

After their mom gives Ann $20 and her sister $60, Ann has twice as much money as her sister.

After receiving that money, Ann's total amount becomes "x + $198 + $20", which simplifies to "x + $218".
Similarly, her sister's total amount becomes "x + $60".

According to the second statement, after receiving the money, Ann has twice as much money as her sister, so we can create the following equation:

x + $218 = 2 * (x + $60)

Simplifying the equation:
x + $218 = 2x + $120

Now, let's solve for x:

Isolating the variables on one side of the equation, we subtract x from both sides:

$218 = x + $120

Subtracting $120 from both sides:

$218 - $120 = x

$98 = x

So, the original amount of money that Ann's sister had is $98.

To find out how much money Ann had at first, we can substitute x = $98 into the expression for Ann's money (x + $198):

Ann's original amount = $98 + $198 = $296

Therefore, Ann had $296 at first.

Answer 3

Let's represent the amount of money Ann had at first as "A" and the amount her sister had as "S."

According to the problem, Ann has $198 more than her sister, so we can write the equation:

A = S + 198 -- (Equation 1)

After their mom gives Ann $20 and her sister $60, Ann has twice as much money as her sister, so we can write the second equation:

A + 20 = 2(S + 60) -- (Equation 2)

Now, let's solve the system of equations to find the value of A.

Substituting Equation 1 into Equation 2, we get:

(S + 198) + 20 = 2(S + 60)
S + 218 = 2S + 120

Moving all the terms involving S to one side, we have:

2S - S = 218 - 120
S = 98

Substituting the value of S back into Equation 1, we can find the value of A:

A = 98 + 198
A = 296

Therefore, Ann had $296 at first.