Jim and Ashley each opened a savings account today. Jim opened his account with a starting amount of $$ \$ 510 $$, and he is going to p in $$ \$ 80 $$ per month. Ashley opened her account with a starting amount of $$ \$ 590 $$, and she is going to put in $$ \$ 60 $$ 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 Jim's account (in dollars) $$ =\square $$ Amount of money in Ashley's account (in dollars) $$ =\square $$ (b) Write an equation to show when the two accounts would have the same amount of money.

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Given:
- Jim's starting amount: $510
- Jim's monthly deposit: $80
- Ashley's starting amount: $590
- Ashley's monthly deposit: $60

(a) To find the amount of money in each account after $$ x $$ months, we can use the formula for the amount of money in a savings account:
$$ \text{Amount} = \text{Starting Amount} + (\text{Monthly Deposit} \times \text{Number of Months}) $$

For Jim's account:
$$ \text{Amount in Jim's account} = 510 + (80 \times x) $$

For Ashley's account:
$$ \text{Amount in Ashley's account} = 590 + (60 \times x) $$

(b) To find when the two accounts would have the same amount of money, we need to set the expressions for the amount of money in each account equal to each other and solve for $$ x $$:
$$ 510 + (80 \times x) = 590 + (60 \times x) $$

Let's solve this equation to find the value of $$ x $$ when the two accounts would have the same amount of money.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$510+80x=590+60x$$
- step1: Move the expression to the left side:
  $$80x-60x=590-510$$
- step2: Add and subtract:
  $$20x=590-510$$
- step3: Add and subtract:
  $$20x=80$$
- step4: Divide both sides:
  $$\frac{20x}{20}=\frac{80}{20}$$
- step5: Divide the numbers:
  $$x=4$$
The value of $$ x $$ when the two accounts would have the same amount of money is $$ x = 4 $$ months.
(a) - Jim's account: $$ 510 + 80x $$ - Ashley's account: $$ 590 + 60x $$ (b) When the two accounts have the same amount of money: $$ 510 + 80x = 590 + 60x $$

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