Question

Henry is saving money for college. He earns $210 each week working part time after school and the weekends. Henry currently has $2,240 in savings. His parents put $100 in his savings account each week and he saves one-third of his paycheck each week. Which expression represents the situation. (n represents the number of weeks)

Answer 1

2,240 + 170n so the he started wit 2,240 with saving 1/3 of his paycheck every week and his parents putting 100 in his account he is saving a total of 170 per week

Answer 2

`f(n)=2240+((170)/(Week)).n`

Explanation:

In order to make an expression that represents the situation we need to make a function that represents Henry's savings.

This will be a function ''f(n)'' because it will depend of the variable ''n'' which is the number of weeks.

Let's start making the function by reading the problem.

''He earns $210 each week working part time after school and the weekends''

We can write :

`f(n)=((210)/(Week)).n`

Where ''210'' is actually $210

''Henry currently has $2240 in savings'' ⇒ We need to add this amount of money to the function.

`f(n)=((210)/(Week)).n+2240`

''His parents put $100 in his savings account each week and he saves one-third of his paycheck each week'' ⇒ We need to add ($100).n to the expression due to his parents and multiply by
`(1)/(3)` the expression that represents its paycheck ⇒

`f(n)=((1)/(3).(210)/(Week)).n+2240+((100)/(Week)).n`

Now, if we work with the expression :

`f(n)=((70)/(Week)).n+2240+((100)/(Week)).n`

`f(n)=2240+((170)/(Week)).n`

Where the units of ''2240'' and ''170'' are $.

That is the final expression which represents the situation.