Question

Greg and Laura each opened a savings account today. Greg opened his account with a starting amount of $590, and he is going to take out $35 per month.

Laura opened her account with a starting amount of $790, and she is going to take out $55 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in t
the account after x months.
Amount of money in Greg's account (in dollars) = ?
Amount of money in Laura's account (in dollars) = ?
(b) Write an equation to show when the two accounts would have the
same amount of money.

Answer 1

a)
Amount of money in Greg's account (in dollars) = 590 - 35x

Amount of money in Laura's account (in dollars) = 790 - 55x

b)
x = 10

Account balances equal after 10 months

Explanation:

We are told x is the number of months after today

Part a

Greg starts off with a balance of $590 and withdraws $35 per month
Total withdrawals in x months for Greg = 35x
Amount of money in Greg's account (in dollars) = 590 - 35x

Laura starts off with a balance of $790 and withdraws $55 per month
Total withdrawals in x months for Laura = 55x
Amount of money in Laura's account (in dollars) = 790 - 55x

Part b

Both accounts will have the same amount of money when Greg's balance equation = Laura's balance equation

590 - 35x = 790 - 55x

Add 35x on both sides:
590 - 35x + 35x = 790 - 55x + 35x
590 = 790 - 20x

590 - 790 = 790 - 790 + 20x
-200 = -20x

Switch sides without affecting the equation:
-20x = -200

Multiply both sides by -1, the signs change from -ve to +ve
20x = 200

x = 200/20

x = 10