Cell Phone Carrier Math Problem

Question

Dhruv purchased a smartphone from a cellphone carrier in March. A monthly

wir4eless bill that he expects to get from the cell phone carrier consists of a wireless

phone service fee and an internet access fee. Dhruv made more calls to his

classmates and used more 4G LTE data in May than he did in April. So the wireless

phone service fee and the internet access fee in May were increased by 15% and 30%

from the wireless phone service fee and the internet access fee in April, respectively.

A wireless bill in May was 25% more than a wireless bill in April.

What percent is the wireless bill in April less than the wireless bill in May?

Round the answer to the nearest integer.

If the account of the wireless bill in May was $ 52.50, what is the amount, in

dollars, of the internet access fee in May? Round the answer to the nearest

tenth.

Answer 1

This question's wording is kind of wacky, but I'm going to assume that the "wireless bill" is the total of the phone and internet bill.

Let m represent May and A represent April:

m = 1.25a so a = m/1.25

m divided by 1.25 is the same as m times 1/1.25 which equals 0.8

So a = 0.8m

In other words, a is 80% of m.

There may be a shorter way, but this is how I solved it:

If we say x is his phone fee in April and y is his internet fee in April, then his total fee in April equals x + y and his total fee in May equals 1.15x + 1.30y. If his total fee in May was 25% more than his total fee in April, then (x + y) times 1.25 also equals his total fee in May:

1.25(x + y) = 1.15x + 1.30y or 1.25x + 1.25y = 1.15x + 1.30y

To find the ratio of x to y, we can set them equal to each other:

1.25x + 1.25y = 1.15x + 1.30y so,

0.1x = 0.05y

x = 0.5y

Now we can plug this for x in an expression we made for the total fee in May and set it equal to 52.50.

1.15x + 1.3y = 52.50

1.15(0.5y) + 1.3y = 52.50

0.575y + 1.3y = 52.50

1.875y = 52.50

y = $28

Now plug this in to solve for x:

1.15x + 1.3(28) = 52.50

x = $14

We can check our work by plugging x and y into an equation for April's fee times 1.25 (which is also equal to May's fee):

1.25(14 + 28) = $52.50

BUT WAIT THERE'S MORE

Remember, we said x and y were values for April. We need values for May:

1.15(14) = $16.1

1.30(28) = $36.4

We can check our work again by adding these two numbers which should be 52.50 and then taking %80 to get 14 + 28 (April's total bill):

16.1 + 36.4 = 52.50

52.50 x 0.8 = 42

and 14 + 28 = 42

Bonus check: Is $52.50 25% more than $42?

42 x 1.25 = 52.5

I like this problem. It's clever.