Let's solve the problem step by step.
(a) Write an Equation
Let \( x \) represent the amount of one of Sheila’s deposits.
Since Sheila made 6 deposits, the total amount she deposited is: \[ 6x \]
Sherri made 5 deposits, and each of her deposits was \( x + 10 \). Therefore, the total amount Sherri deposited is: \[ 5(x + 10) \]
According to the problem, both sisters deposited the same amount in the end, so we can set up the equation: \[ 6x = 5(x + 10) \]
(b) Solve the Equation
Now, we will solve the equation \( 6x = 5(x + 10) \).
Step 1: Distribute the 5 on the right-hand side: \[ 6x = 5x + 50 \]
Step 2: Subtract \( 5x \) from both sides: \[ 6x - 5x = 50 \] \[ x = 50 \]
So, Sheila deposited \( x = 50 \) dollars each time.
(c) Check Your Solution
Now let's check the solution by calculating the total deposits for both sisters:
Sheila: \[ \text{Total deposited by Sheila} = 6 \times 50 = 300 \text{ dollars} \]
Sherri: The amount of each of Sherri's deposits is: \[ x + 10 = 50 + 10 = 60 \text{ dollars} \] Now calculate the total deposited by Sherri: \[ \text{Total deposited by Sherri} = 5 \times 60 = 300 \text{ dollars} \]
Both sisters deposited the same total amount, confirming that our solution is correct.
(d) State the Solution in Very Small Complete Sentences
Sheila deposited $50 each time. Sherri deposited $60 each time. Both sisters deposited the same total amount: $300.