Answer to Question #132237 in Algebra for Geraldo

Question

Mae has a $25 gift card that loses $3 each month. She also has a $40 gift card that loses $5.5 each month that she is not using it. At what month will the value of both cards be equal?

Answer 1

As per the question,

for 25$ card

The arithmetic progression is,

25,22,19,16...

where first term a=25

common difference d=-3

Let after n months Their both cards are equal

So n$^{th}$ is given by,

t$_n$ =a+(n-1)d

=25+(n-1)(-3)

=25-3n+3

=28-3n...(1)

for 40$ gift card, The arithmetic progression are as follows.

40,34.5,29,23.5....

where first term a=40

and common difference d=-5.5

Their n$^{th}$ term is given by,

t$_n=$ a+(n-1)d

=40+(n-1)(-5.5)

=45.5-5.5n

Let equate both the n term equally,

28-3n=45.5-5.5n

5.5n-3n=45.5-28

2.5n=17.5

n=7

so month is n-1 i.e 6

Hence After 6 month from now Her card became equal.