Answer:
[tex]f(n)=2240+(\frac{170}{Week}).n[/tex]
Step-by-step 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 :
[tex]f(n)=(\frac{210}{Week}).n[/tex]
Where ''210'' is actually $210
''Henry currently has $2240 in savings'' ⇒ We need to add this amount of money to the function.
[tex]f(n)=(\frac{210}{Week}).n+2240[/tex]
''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 [tex]\frac{1}{3}[/tex] the expression that represents its paycheck ⇒
[tex]f(n)=(\frac{1}{3}.\frac{210}{Week}).n+2240+(\frac{100}{Week}).n[/tex]
Now, if we work with the expression :
[tex]f(n)=(\frac{70}{Week}).n+2240+(\frac{100}{Week}).n[/tex]
[tex]f(n)=2240+(\frac{170}{Week}).n[/tex]
Where the units of ''2240'' and ''170'' are $.
That is the final expression which represents the situation.
