Question

4 points) 3. At the bank, Sheila made 6 deposits, each in the same amount. Her sister Sherri made 5 deposits, each in the same amount. Each of Sherri's deposits was $10 more than each deposit Sheila made. Both sisters deposited the same amount in the end. How much did each sister deposit each time? (a) Write an equation. Let x represent the amount of one of Sheila’s deposits. (b) Solve the equation. Show your work. (c) Check your solution. Show your work. (d) State the solution in complete sentences. Answer:

Answer 1

6x = 5(x + 10)
6x = 5x + 50
6x - 5x = 50
x = 50

check...
6(50) = 5(50 + 10)
300 = 300....correct

Sheila made 6 deposits of $ 50 each...totaling $ 300. Sherri made 5 deposits of $ 60 each....totaling $ 300.

Answer 2

Lets x = the amount Sheila's deposit each time

So 6 deposits = 6x

Sheila's sister deposits was $10 more each deposit Sheila made, then her sister deposit amount each time should be: x +10

Sheila's sister made 5 deposits: 5(x+10)

Both sisters deposited the same amount in the end:

6x = 5(x+10)

6x = 5x + 50

Now you can add (-5x) to both sides:

6x + (-5x) = 5x + 50 + (-5x)

6x - 5x = 5x + 50 - 5x

Simplify both sides:

x = 50

So Sheila deposits each time: $50

Sheila's sister deposits each time: x + 10 = 50 +10 = 60

Double check:

Sheila deposits 6 times = 6 x 50 = 300

Sheila's sister deposits 5 times = 60 x 5 = 300

Both deposited $300 (same amount) in the end.