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.