Question

At the beginning of the year, Alexa had $40 in savings and saved an additional $14 each week thereafter. Joshua started the year with $70 and saved $8 every week. Let AA represent the amount of money Alexa has saved tt weeks after the beginning of the year and let JJ represent the amount of money Joshua has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the amount of money Alexa and Joshua have saved in the week that they have the same amount of money saved.

Answer 1

110 dollars

Explanation:

First equation: 14t+40

Second equation: 8t+70

Then find the value of t.

Equation: 14t+40= 8t+70

t=5. Then substitute the value of t into the first equation to get your final answer.

Answer 2

`A=40+14t`

`J=70+8t`

Amount of money Alexa and Joshua have saved in the week that they have the same amount of money saved is equal to $110.

Explanation:

Initial amount as savings in account of Alexa = $40

Amount saved per week by Alexa = $14

Initial amount as savings in account of Joshua = $70

Amount saved per week by Joshua = $8

Amount saved by Alexa
`t` weeks after the beginning of the year (A) =
`\$(40+14t)`

`A=40+14t`

Amount saved by Joshua
`t` weeks after the beginning of the year (J) =
`\$(70+8t)`

`J=70+8t`

Now solve
`40+14t=70+8t`.

`70-40=14t-8t\\30=6t`

t = 5 years

`A=40+14(5)=40+70=\$110\\J=70+8(5)=70+40=$110`