Question

Peter and Sam both opened a savings account when they got their first job. Peter started with 150 in his account and deposits $30 each week. Sam started with $90 in his account and deposits $45 each week. Let x represent the number of weeks and y represent the total amount of money in the account. Write a system of equation. Equations for Peter:Equations for Sam: 2. Peter and same will have the same amount in their account at _____ weeks. At this time they will both have $_____ in their accounts

Answer 1

For the given question, Let x represent the number of weeks and y represent the total amount of money in the account.

Peter and Sam both opened a savings account when they got their first job.

Peter started with 150 in his account and deposits $30 each week.

So, the equation of Peter will be:

`y_1=30x+150`

Sam started with $90 in his account and deposits $45 each week.

So, the equation of Sam will be:

`y_2=45x+90`

2. we will find when Peter and same will have the same amount in their account

so,

`\begin{gathered} y_1=y_2 \\ 30x+150=45x+90 \end{gathered}`

Solve the equation to find the value of (x):

`\begin{gathered} 30x-45x=90-150 \\ -15x=-60 \\ \\ x=(-60)/(-15)=4 \end{gathered}`

Substitute with (x) into equation y1 or y2 to find the amount in their account

so,

`y_1=30\cdot4+150=120+150=270`

So, the answer will be:

Peter and same will have the same amount in their account at 4 weeks. At this time they will both have $270 in their accounts