Question

Pls answer quickly Due in 2

Jake and Seth put some money into their money boxes every week. The amount of money (y), in dollars, in their money boxes after a certain amount of time (x), in weeks, is shown by the equations below:

Jake: y = 5x + 85
Seth: y = 20x + 40

After how many weeks will Jake and Seth have the same amount of money in their money boxes and what will that amount be?

Answer 1

3 weeks

$100

Explanation:

Given system of equations:

`\begin{cases}\textsf{Jake:}\;\; y = 5x + 85\\\textsf{Seth:}\;\; y = 20x + 40\end{cases}`

where:

• x is time (in weeks).
• y is the amount of money in the money box (in dollars).

To find after how many weeks Jake and Seth will have the same amount of money in their money boxes, solve the given system of equations for x by the method of substitution.

`\begin{aligned}20x+40&=5x+85\\20x+40-5x&=5x+85-5x\\15x+40&=85\\15x+40-40&=85-40\\15x&=45\\15x / 15 &=45/ 15 \\x&=3\end{aligned}`

Therefore, Jake and Seth will have the same amount of money in their money boxes after 3 weeks.

To determine what that amount will be, substitute the found value of x = 3 into one of the equations and solve for y:

`y=5x+85`

`y=5(3)+85`

`y=15+85`

`y=100`

Therefore, Jake and Seth will both have $100 in their money boxes after 3 weeks.