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. c. check your solution.

TLDR: Equation is 5(10 + x) = 6x. x = 50, so Sheila deposited $50 each 6 trips. Sherri deposited $60 each 5 trips. Both of them deposited $300 in total.

Sherri deposited $10 more into her bank account than Sheila each 5 times. Expression: 5(x + 10).

Sheila deposited money 6 times
Expression: (6)(x) or 6x

Put it all together and the equation is 5(x+10)=6x. 

Solve by distributing the 5 on the right side of the equation 5(x+10) to get 5x + 50 = 6x. Subtract 5x on both sides of equation. 5x - 5x + 50 = 6x - 5x to get 50 = 1x. Divide by 1 on each side to isolate the variable. x = 50. Sheila paid $50 in each of her 6 deposits, so she deposited $300 in total. Check the equation by replacing x with 50. 

Sherri paid $60 in each of her 5 deposits because 50 + 10 is 60. 60 by 5 is also $300.