Delila has $1200 in a saving account and in a checking account. The ratio of money in saving to money in the checking is 3 to 2. Use a system of equation to find how much money is in each account .

Question

Delila has $1200 in a saving account and in a checking account. The ratio of money in saving to money in the checking is 3 to 2. Use a system of equation to find how much money is in each account .

Answer 1

Let's assume the amount of money in the saving account is S, and the amount of money in the checking account is C.

According to the given information:
- The total amount of money in both accounts is $1200, so we have: S + C = 1200. (Equation 1)
- The ratio of money in the saving account to money in the checking account is 3 to 2, so we have: S / C = 3 / 2. (Equation 2)

To solve this system of equations, we can use the method of substitution.

Step 1: Solve Equation 2 for S:

S / C = 3 / 2
Cross-multiplying, we get:
2S = 3C
S = (3/2)C

Step 2: Substitute the value of S in Equation 1:

(3/2)C + C = 1200
Multiplying through by 2 to eliminate fractions, we get:
3C + 2C = 2400
5C = 2400
C = 2400 / 5
C = 480

Step 3: Substitute the value of C back into Equation 1 to find S:

S + 480 = 1200
S = 1200 - 480
S = 720

Therefore, Delila has $720 in the saving account and $480 in the checking account.

Answer 2

To solve this problem using a system of equations, we can set up two equations based on the given information.

Let's assume "x" represents the amount of money in Delila's saving account, and "y" represents the amount of money in Delila's checking account.

1. The first equation represents the total amount of money she has in both accounts:
x + y = 1200

2. The second equation represents the ratio of money in the saving account to money in the checking account:
x/y = 3/2

To solve this system of equations, we can use the method of substitution or elimination.

For simplicity, let's solve it using the substitution method. We can solve the first equation for "x" and substitute it into the second equation:

From the first equation, we have x = 1200 - y

Substituting this into the second equation, we have:
(1200 - y) / y = 3/2

Now, we can cross-multiply and solve for "y":
2(1200 - y) = 3y
2400 - 2y = 3y

Moving all terms to one side, we get:
2400 = 5y + 2y
2400 = 7y

Dividing by 7, we find:
y = 2400 / 7
y ≈ 342.86

Now that we have the value of "y", we can substitute it back into the first equation to find the value of "x":
x + (342.86) = 1200
x ≈ 1200 - 342.86
x ≈ 857.14

Therefore, Delila has approximately $857.14 in her saving account and $342.86 in her checking account.