Question

Karen and Maria each open a savings account at the same time. They only make deposits into their accounts and do not make withdrawals. When Karen opens her account she deposits $28 into it. She then deposits $5 into her account each week. The total amount of money (y), in dollars, in Maria’s account x weeks after it is opened is described by the function y=8x+7.​ What is the total amount of money that each girl has in her account 2 weeks after they have the same amount of money in their accounts?

Answer 1

The amount in Maria's account is $79.

The amount in Karen's account is $73.

Step-by-step explanation:

Karen deposits $28 into her account and she deposits $5 each week into her account.

From this given information, the equation can be framed as y = 28+5x ----(1)

where,

• y is the total amount deposited.
• x is the number of weeks the particular amount is deposited.

The equation for Maria's account is given as y = 7+8x ------(2)

To find the no.of weeks at which they both have same amount of money :

Equating the equations (1) and (2),

⇒ 28 + 5x = 7 + 8x

⇒ 28-7 = 8x-5x

⇒ 21 = 3x

⇒ x = 21/3

⇒ x = 7 weeks

After 7 weeks, the money in the account of Karen & Maria will be same.

To find the amount of money in each girl's account after 2 weeks :

It is given that, you have to calculate amount of money that each girl has in her account 2 weeks after they have the same amount of money in their accounts.

We already know that, it takes 7 weeks for them to have same amount.

So, 7 weeks + 2 weeks = 9 weeks

You have to calculate the amount in each girl's account after 9 weeks.

Karen's account :

Substitute x=9 in eq(1),

⇒ y = 28+5(9)

⇒ y = 28+45

⇒ y = 73

The amount in Karen's account is $73.

Maria's account :

Substitute x=9 in eq(1),

⇒ y = 7+8(9)

⇒ y = 7+72

⇒ y = 79

The amount in Maria's account is $79.

Answer 2

The amount left with both of them post two weeks would be as follows

C). Karen has $73. Maria has $79

Find the amount

Given that,

Amount deposited by Karen = $28 and $5 every week

so,

Assuming the total deposited amount as y and x being the week count, the equation would be:

$y = 28+5x$  ...(i)

Using the same concept, the equation for Maria would be:

$y=8x+7$   ...(ii)

by solving the equations (i) and (ii), we get the value of $x$,

$28 + 5x = 7 + 8x$

⇒ $28-7 = 8x-5x$

⇒ $21 = 3x$

∵ $x = 7 weeks$

We know that post 7 weeks, the amount in both accounts would remain same.

The total duration would be:

$7 + 2 = 9 weeks$

By putting the value of 9, we can find the amount in their accounts as:

Karen

$y = 28 + 5(9)$

∵ $y = 73$

Maria

$y=8(72)+7$

∵ $y = 79$

Thus, option C the correct answers.

Learn more about "Function" here:

brainly.com/question/5245372

The options are missing which are provided as follows:

Karen has $45. Maria has $72.

Karen has $58. Maria has $55.

Karen has $73. Maria has $79

Karen has $185. Maria has $128