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So when does math make you crazy in your everyday life? Are there situations that make your hands sweat?

On selected Fridays, I’ll host an open thread where you can ask your questions or share your specific frustrations with everyday math. And if you see a question from someone else that you can answer? Go for it! I’ll select questions for future posts here at Math For Grownups. In those posts, I’ll show you easy ways to get around these frustrations.

So let ‘er rip in the comments section. Ask about fractions or grocery store math or the best way to place a bet on the ponies. Just remember that we’re not here to do your homework for you. And leave your calculus, trig and diff eq questions for another blog.

Whatcha got?

Susan Weiner says

Sines, cosines…what do those things mean?

Laura says

Yeah, Susan! Whoever thought it was a good idea to add *words* like sine, cosine and tangent to math? We should only be dealing with numbers!

Sine, cosign and tangent are functions. You probably heard about them for the first time in your geometry class, when you were working with right triangles. See, there are special relationships between the sides of a right triangle, and it turns out these relationships are constant. That’s where sine, cosine and tangent were born. These functions can be used to find the length of a side of a right triangle.

But they’re probably even more useful in various sciences. That’s because, when they’re graphed, sine and cosine look like waves — yep, like sound and light waves. (Tangent looks like a series of stretched out S-es.)

So, what does the average person need to know about sine and cosine? I’d say three things: 1) They’re functions, 2) They can help you find the length of the side of a right triangle and 3) They look like waves when they’re graphed on an x-y plane.

If you really need to use them, you can look the rest up!

Susan Weiner says

Thank you, Laura! I know more than I ever learned in geometry class.

Gretchen says

Hi Laura, I have a math question for grownups. My husband’s company does not provide health insurance for me and the kids, which is a $12,000 value. In his field, there is a salary scale based on education, number of years experience, geography, etc. The salary scale assumes that the employer provides health insurance for the family. His salary is currently at 79% of the scale, and his employer wants to eventually get him up to 100%. But that doesn’t include the insurance, so it won’t really be at 100% and is not now really at 79%. But I can’t figure out which way to do the math so he can show them the actual percentage. They’re saying he’s at 79 percent. I’m saying it’s lower because they aren’t accounting for that $12K, but I can’t figure out the math formula to calculate the actual percentage. Does this make sense?

Laura says

Great question, Gretchen! And I have to say it’s a toughie. There are two steps to this problem:

1. Find the actual salary that is at 100% of the scale. (If you already know this, you can skip this step.)

2. Find the actual percent of your husband’s salary, minus the cost of insurance.

(And here’s where I am compelled to make a disclaimer. Remember, *your* cost of insurance will be different from the company’s cost of insurance. In general, it costs the company less money to pay for your insurance than it would for you to buy it elsewhere. So, using the $12,000 figure may not be an accurate representation of the scale.)

To do steps 1 and 2, you need to use proportions. Proportions are merely two equal ratios or fractions. A big clue that you’ll need proportions is that you’re using percents. That’s because 79% is the same as 79/100.

(And here’s another disclaimer. I don’t know how to write vertical fractions in comments yet. So when I say 1/2, for example, I mean one half. Make sense?)

The hard part is figuring out what the proportions should be:

1. salary/x = 79/100, where “salary” is your husband’s salary, and x is the top salary on the scale. That’s because your company assumes that your husband’s salary is 79% of the scale. (So “salary” and “79” are in the numerators — or top values of the fractions.)

To solve this proportion, you need to plug in your husband’s salary and then solve for x. In order to make this easy to explain, I’m going to assume that his salary is $100,000.

substitute: $100,000/x = 79/100

cross multiply: $100,000 times 100 = 79x

simplify: $10,000,000 = 79x

solve for x: $126,582 = x (I just divided each side of the equation by 79)

So in this example, the top salary would be $126,582.

2. $100,000 – 12,000/126,582 = p/100, where p is the actual percent of the scale.

To get this proportion, you subtract the insurance from your husband’s salary and put it over the max salary for the scale. Then you set that equal to x/100. Notice that your husband’s actual take home (his salary minus the insurance) is on top, as well as p. And that the max salary and 100 are on the bottom. Now you can solve for p, as you did in the previous proportion:

simplify: $88,000/126,582 = p/100

cross multiply: $88,000 times 100 = 126,582p

simplify: $8,800,000 = 126,582x

solve for x: 69.6 = p (I just divided each side of the equation by 126,582)

So what does this mean? If your husband makes $100,000 a year and is paying $12,000 for insurance, he’s earning 69.5% of the salary scale.

This may look really, really complicated, but it’s not really. Part of the problem may be that it’s difficult to show the proper math notation. And part of it is that I didn’t know what 100% of the scale was.

But if you’re confused, don’t hesitate to ask again! *smile* Hope this helps a little.

Gretchen says

Thanks! This is so helpful. Oh, and the $12,000 figure is exactly what they would pay for me and the kids. I know this because I had to go on the insurance when I was pregnant, and I wrote those checks myself. 🙂