Question

Jim has $310 in his savings account and adds $4 per week. At the same time, Rhonda has $260 in her savings account and adds $9 per week. (a) How long will it take for Rhonda to have the same amount as Jim? Weeks (b) How much will each have?

Answer 1

a) After 10 weeks Jim and Rhonda will have the same amount.

b) They both would have $350 in their account after 10 weeks.

Explanation:

Given:

Amount Jim has = $310

Amount Jim adds per week = $4

Let the number of weeks be 'x'.

So we can say that;

Total amount Jim will have after 'x' week will be equal to amount Jim has plus amount Jim adds per week multiplied by number of weeks.

framing in equation form we get;

Total amount Jim will have after 'x' week =
`310+4x`

Also Given:

Amount Rhonda has = $260

Amount Rhonda adds per week = $9

So we can say that;

Total amount Rhonda will have after 'x' week will be equal to amount Rhonda has plus amount Rhonda adds per week multiplied by number of weeks.

framing in equation form we get;

Total amount Rhonda will have after 'x' week =
`260+9x`

a) We need to find the number of weeks in which the both will have same amount;

Now to find number of weeks in which the both bill have same amount;

we have to make both the equation equal and solve the same we get;

`310+4x =260+9x`

Combining the like terms we get;

`9x-4x=310-260\\\\5x=50`

Now using Division property of equality we will divide both side by 5 we get;

`(5x)/(5)=(50)/(5)\\ \\x =10`

Hence After 10 weeks Jim and Rhonda will have the same amount.

b) We have to find amount they would have after 10 weeks.

To find the same we will substitute value of 10 in each equation we get;

Total amount Jim will have after '10' weeks =
`310+4x = 310+4*10 =310 +40 =\$350`

Total amount Rhonda will have after '10' weeks =
`260+9x = 260+9* 10 =260+90 =\$350`

Hence They both would have $350 in their account after 10 weeks.