(a) A cube of osmium metal 1.500 cm on a side has a mass of 76.31 g at 25 °C. What is its density in g>cm3 at this tempera-
ture? (b) The density of titanium metal is 4.51g>cm3 at 25 °C.

What mass of titanium displaces 125.0 mL of water at 25 °C?

Scientific method

Scientific method

50

Step-by-step explanation:

FIRST, we need variables. Once we define variables, it's much easier to turn this word problem into a math problem.

Let a = first side

Let b = second side

Let c = third side

NOW, we can turn the words into equations:

"a triangle has a perimeter of 165 cm."

a + b + c = 165

"the first side is 65cm less than twice the second side."

a = 2b - 65

"the third side is 10cm less than the second side."

c = b - 10

Before we finish, I have to ask: Who writes problems like this??? Pointless problems like these are why kids don't like math! Ugh. Drives me crazy. It's a shame, because solving math problems really does have a certain satisfaction, once you learn how. [Okay. I'm done. Back to the problem.]

If we could get this to have only one variable, we could solve it. Substitution to the rescue!

a + b + c = 165 (rewrote equation from above)

(2b - 65) + b + (b - 10) = 165 (substituted "a" and "c" from equations above)

See how that works? Let's solve it.

2b - 65 + b + b - 10 = 165 (dropped the parentheses, because there was nothing to distribute, not even a minus sign)

4b - 75 = 165 (combined like terms)

4b = 240 (added 75 to both sides)

b = 60 (divided both sides by 4)

We found the second side! We can find the first and third sides using those equations from above:

a = 2b - 65

a = 2*60 - 65

a = 120 - 65

a = 55

c = b - 10

c = 60 - 10

c = 50

All done