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Kathleen Q.

Math tutor for 5 years, continuing education to become a math and science teacher

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Pre-Algebra

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Question:

How would you solve 3+(2+6)^2+9/3 using the Order of Operations?

Kathleen Q.

Answer:

First, we solve what in inside the parenthesis so our next expression is 3+(8)^2+9/3. Next, we solve the exponents so our next expression is 3+64+9/3. Next, we do division so the next expression will be 3+64+3. Now just solve the expression by adding all the numbers together. The answer is 70.

Basic Math

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Question:

Kelly goes to the grocery store with $1. Each apple is 20 cents and each banana is 60 cents. How many apples and bananas can she get for $1.

Kathleen Q.

Answer:

First, we create variables for the apples and bananas. Let's say a for apple and b for banana. Now let's create an equation based on the statement, $1 = .20a+.60b. Now we will guess and check to find a and b to equal to $1. $1 = .20(1)+.60(1) which equals .80 so we need to raise it by .20 to get $1. So our final completed equation is $1 = .20(2)+.60(1). So Kelly can by 2 apples and 1 banana for $1.

Algebra

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Question:

If x varies inversely proportionally to the square root of y, and x=4 and y=16. Find y when x=2.

Kathleen Q.

Answer:

First, we need to set up the two sides of the given equation. In this type of problem there is an unstated constant, k. For the variable x, "inversely" means that x will be in the denominator like so 1/x. Now the variable y is under a square root, also written like so y^(1/2). Now to combine the two sides and add the constant k, (k/x)=y^(1/2). Second we enter the given information, (k/4)=16^(1/2). Now we know that the square root of 16 is 4 and we should multiply the x-term, 4 to isolate k. Now we have k=16. Third step is to solve the problem for y, so now we have (16/2)=y^(1/2). This resolves to 8^2=y, and so y=64.

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