Ann had $198 more than her sister. After their mother gave Ann $20 and her sister $60, Ann had twice as much money as her sister. How much money did Ann have at first.

Question

Ann had $198 more than her sister. After their mother gave Ann $20 and her sister $60, Ann had twice as much money as her sister. How much money did Ann have at first.

Answer 1

a = s+198

(a+20) = 2(s+60)
a = 296

so, Ann started out with $296.

Answer 2

Let's set up an equation to solve this problem step-by-step.

Let's say Ann's initial amount of money is "A" dollars, and her sister's initial amount of money is "S" dollars.

According to the problem, Ann had $198 more than her sister, so we can write the first equation as:
A = S + $198 ----(Equation 1)

After their mother gave Ann $20 and her sister $60, Ann had twice as much money as her sister. We can write the second equation as:
A + $20 = 2(S + $60) ----(Equation 2)

Now, let's solve the system of equations (Equations 1 and 2) step-by-step:

Step 1: Substituting the value of A from Equation 1 into Equation 2, we get:
S + $198 + $20 = 2(S + $60)

Step 2: Simplifying the equation:
S + $218 = 2S + $120

Step 3: Moving all the terms involving S to one side:
2S - S = $218 - $120
S = $98

So, Ann's sister had $98 initially.

Step 4: Substituting the value of S into Equation 1 to find Ann's initial amount:
A = S + $198
A = $98 + $198
A = $296

Therefore, Ann had $296 initially.

Answer 3

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

Let's assume that Ann initially had x dollars and her sister had y dollars. According to the first sentence, Ann had $198 more than her sister, so we can write the equation:

x = y + 198

After their mother gave Ann $20 and her sister $60, Ann had twice as much money as her sister. From this information, we can write another equation:

x + 20 = 2(y + 60)

Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.

Substituting the value of x from the first equation into the second equation, we get:

(y + 198) + 20 = 2(y + 60)

Simplifying the equation, we get:

y + 218 = 2y + 120

Rearranging the equation, we have:

2y - y = 218 - 120

y = 98

Substituting the value of y back into the first equation, we can find the value of x:

x = 98 + 198

x = 296

Therefore, Ann initially had $296.