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:

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

To solve the equation 350r = 367.50, you need to divide both sides by 350 to isolate r:

350r = 367.50
r = 367.50 / 350
r ≈ 1.05

So, the value of r that would make sense in this equation is approximately 1.05, not 1.1.

If you multiply 1.05 by $350, you will indeed get $367.50 which represents Niko's final amount after a 5% increase on his savings.

Answer 3

To find the value of r, you need to solve the equation 350r = 367.50 for r. Let's go through the steps together:

Step 1: Divide both sides of the equation by 350:
350r / 350 = 367.50 / 350
r = 1.05

So, the correct value of r is 1.05, not 1.1.

To verify that this value makes sense, let's calculate the final amount Niko would have using this value of r:

Starting amount: $350
Percentage increase: 5% (equivalent to multiplying by 1.05)

Final amount = Starting amount x (1 + Percentage increase)
Final amount = $350 x (1 + 0.05)
Final amount = $350 x 1.05
Final amount = $367.50

As you can see, by multiplying the initial amount ($350) by 1.05, you indeed get $367.50, which matches the result you obtained through calculations. Therefore, the number 1.05 is the correct value for r in this context.

Answer 4

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