Question

Raina and Keith each opened a savings account today. Raina opened her account with a starting amount of $180, and she is going to put in $70 per month.

Keith opened his account with no starting amount, and he is going to put in $100 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in
the account after x months.
Amount of money in Raina's account (in dollars) -
Amount of money in Keith's account (in dollars) = 0
(b) Write an equation to show when the two accounts have the same
amount of money.
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Answer 1

Explanation:

(a) For Raina's account:

The starting amount is $180, and she adds $70 per month. So, the expression for the amount of money in Raina's account after x months is:

Amount = $180 + $70x

For Keith's account:

The starting amount is $0, and he adds $100 per month. So, the expression for the amount of money in Keith's account after x months is:

Amount = $100x

(b) To find when the two accounts have the same amount of money, we can set the expressions equal to each other and solve for x:

$180 + $70x = $100x

To simplify the equation, we can subtract $70x from both sides:

$180 = $30x

Now, divide both sides by $30 to solve for x:

$x = 6

So, the two accounts will have the same amount of money after 6 months.