Question

Niko had his savings increased by 5% this year. He started with $350 in his account and calculated how much he had at the end of the year by using the following sets of calculations:

$350×0.05=$17.50
$350+$17.50=$367.50

Find a single number that Niko could have multiplied his starting amount of $350 by to get $367.50 by solving the equation below for r. Why does this number make sense?

350r=367.50


When i solved this I got r=1.1. Then i multiplied it to 350 but ended up getting 385. Please help me.

Answer 1

divide both sides by 350 and the answer should be 1.05

Answer 2

suppose something costs $x and you increase it by 5%
doing it your ways:
increase = .05x
end result = x + .05x
= x(1 + .05)
= 1.05x

so you get the result after anything is increased by 5% , just multiply by 1.05

or
to get the result after anything is increased by 16% , just multiply by 1.16
or
to get the result after anything is increased by 3.56 % , just multiply by 1.0356

in the same , suppose something is decreased by 7% you could just multiply by .93