Math Is Fun Forum

At the beginning of the month, Mike had a balance of $210 in his checking account. During the next month, he deposited $80, wrote a check for $120, made another deposit of $25, wrote two checks: one for $60 and the other for $32.  He was also assessed a monthly service charge of $5. What was his balance at the end of the month?

At the start of the month Mike had $210.

Deposited $80==> $210 + $80 = $290.

Wrote a check for $120==> $290 - $120 = $170.

Made a deposit of $25==> $170 + $25 = $195.

Wrote two checks: $60 + $32 = $92. So, $195 - $92 = $103.

He was assessed a monthly service charge of $5.

$103 - $5 = $98.

Mike's balance at the end of the month was $98.

Note: This is a very easy BUT TRICKY question. The easier the question, the easier it is to make mistakes.

Convert each number to scientific notation.

A. 32.14

B. 0.0514

Question A

Count left from the decimal point until reaching a number that I will call x, where x lies between 1 and 10.

Doing this, 32.14 becomes 3.214. I now multiply 3.214 by 10 raised to the first power to get a final answer of
3.214 x 10^1.

Why does moving a decimal point to the left creates a positive exponent?

Question B

Count right from the decimal point until reaching a number that I will x, where x lies between 1 and 10.

Doing this, 0.0514 becomes 5.14. I now multiply 5.14 by 10 raised to the negative 2 power to get a final answer of 5.14 x 10^(-2).

Why does moving a decimal point to the right creates a negative exponent?

Given 2y - 1 = 9, find 3y + 7.

Let's first solve 2y - 1 = 9 for y.

2y - 1 = 9

2y = 9 + 1

2y = 10

y = 10/2

y = 5

Now that we know the value of y, we plug 5 for y in the binomial 3y + 7.

Let y = 5

3y + 7

3(5) + 7

15 + 7 = 22

Answer is 22.

If (x^²)^²= 16, what is the value of x?

Well, (x^2)^2 becomes x^4.

x^4 = 16

Take fourth root on both sides of the equation.

4root{x^4} = 4throot{16}

x = 2, x = -2

There are two values of x because I had to take the fourth root. If the fourth root was the given problem, then x = 2.

Is this a good explanation?

Going into the final exam, which will count as 2/3 of the final grade, Larry has test scores of 86, 80, 84, and 90. What score does Larry need on the final exam in order to earn a B, which requires an average score of 80? What does he need to earn an A, which requires an average score of 90?

To Earn An B:

(86 + 80 + 84 + 90 + B)/5 = 80

To Earn An A:

(86 + 80 + 84 + 90 + A)/5 = 90

What do you say about my setup?

A total of $10,000 is to be divided between Sean and George, with George to receive $3000 less than Sean. How much did each receive?

Solution:

Sean will receive x amount.

George will receive x - 3000 amount.

My equation set up is

x + x - 3000 = 10,000

Is this correct?