Dun, dun, DUN!!!!!
Word problems truly are Idiot's Guide's sole deficiency. The only word problems are in the last chapter and deals more with d = rt as opposed to "If Mary has three apples..." I don't need practice with d = rt! I remember that one! I don't remember divining how many apples Mary has out of no practical information! Do I look like Shawn Spencer to you? "Luckily" Everything is rife with them. I rewrote them with a fresh side of snark.
1. Kristen's grandfather was a college math professor for many years and thinks people enjoy his little challenges. He keeps a jar of coins with only quarters, nickels, and dimes. One day Grandpa tells eleven-year-old Kristen, "There's $48.50 in my silver coin jar. The number of Roosevelts is 20 more than the number of Washingtons, and there are 30 more Jeffersons than Roosevelts. If you can figure out how many of each coin there are by the time your mother gets home, you can have the jar."
Real life answer: Kristen waits until Grandpa takes a nap, takes the money, counts the number of coins, and pays the neighboring unemployed CalTech grad in WoW tokens to come up with the needed equation. Grandpa keeps his word and gives her the jar -- but not the money. Because Grandpa is a jerk like that.
2. Sonya's idiot assistant forgot to mail a very important contract to a client. She also didn't pay the internet bill so email is out of the question. Now Sonya has to take it to the client who is 6 hours away. She gets on the interstate at 7 a.m. and sets her cruise control at 65 mph. Minutes later Allison, aforementioned idiot assistant, realizes she forgot to put the contracts in Sonya's briefcase. She flies out the door with the contracts, jumps in her car, and sets off after Sonya. She gets on the interstate at 7:30 a.m. What is the lowest speed she can set her cruise to catch up with Sonya in less than two hours and hopefully keep her job?
Real life answer: Allison catches up with Sonya but is pulled over by a cop as they're exiting the interstate. Allison gets a $150 ticket. Once Sonya secures the contract in her briefcase she fires Allison. As Sonya drives away she neglects to realize she left the briefcase sitting on the road beside her car. Allison snatches it, throwing it in a drainage ditch on her way back home.
I'm running out of snark steam.
3. Xiang, Amy, and Jiang are 3 years apart in age. Xiao is the youngest and Jiang is the oldest. If 30 more than the sum of Xiao's age and Amy's age is 3 times Jiang's age, can Amy vote in the U.S. general election?
Real life answer: Amy is old enough to vote in the US general election, but she won't because she thinks it's pointless. Great civic attitude, Amy.
4. Juanita opens a pottery studio in an upscale area of town. Her expenses for total 15n + 320 per day when she has n pieces of pottery to sell. If Juanita charges $28 per piece, a totally realistic price for handmade pottery, how many pieces must she sell each day to make a profit of at least $100 per day?
Real life answer: After the 1000th customer who (1) claims they could totally make that pot for a third of the price, (2) tries to haggle her down to Walmart prices, and (3) allows their children to break pieces and refuses to pay for the damage, Juanita stages a kiln accident that consumes her entire studio for the insurance money.
Actual Mathematical Answers
1.) Solve for quarters. BUT any expression of x must be multiplied by the value of the coin the expression represents. And despite the book examples don't use q, d, or n. I couldn't get past the coin value using variables representative of the coin names.
#quarters = x
#dimes = 2x + 20 (20 more than 2 times quarters)
#nickels = 2x + 50 (30 more nickels than dimes)
25cents(x) + 10cents(2x + 20) + 5cents (2x + 50) = 4850cents
25x + 20x + 200 + 10x +250 = 4850
55x = 4400
x = 80 quarters (or $20.00)
Now solve the other expressions for x
2(80) + 20 = 180 dimes ($18.00)
2(80) + 50 = 210 nickels ($10.50)
2.) I actually handled this one mostly by myself. Probably because I see it as a physics rather than an algebra problem, and while I don't take road trips I drive a lot. I have to figure out how far Sonya travels in two hours AND how far she travels in her 30 minute head start (expressed as .5 hours) to account for it in Allison's catch up speed.
d = (65)(2)
d = 130mi in 2 hours
d = 65(.5)
d = 32.5mi in .5 hours
The formula for Allison's catch up is what I had to double check. I wasn't completely sure where that head start factored in.
130 = 2r - 32.5
162.5 = 2r
81.25 = r
The book gives this as the accepted answer. I consider the actual answer 82 since (a) Allison needs to catch up in less than 2 hours and 81.25 will take exactly 2 hours (perhaps this is best expressed as 81.25 < r) and (b) how are you going to set your cruise somewhere between 81 and 82 miles?
3. Everything is nice enough to prompt me to solve for Amy's age (a), which makes sense because she's the middle of the group. I know Xiao is three years younger (a - 3) and Jiang is three years older (a + 3). Now what to do with that whole 3 times older than yada yada yada and how to set it up.
[Amy's age (a) + Xiao's age (a - 3)] + 30 = 3(a + 3) Jiang's age
a + (a - 3) + 30 = 3(a + 3)
2a - 3 + 30 = 3a + 9
2a + 27 = 3a + 9
-a = -18
a = 18
4. I totally blew this the first try.
15n + 320 ≤ 28n + 100
15n ≤ 28n - 220
-13n ≤ -220
13n ≤ 220
n ≤ 16.92
Even at $28 a pop that doesn't feel right. *look up answer* *go back in chapter for example* The $100 should've gone with the expense formula, not the retail price. And I don't need the ≥ sign, only the >? But it says at least which usually translates to "equals to"...fine. Whateves.
28n > 15n + 320 + 100
28n > 15n + 420
13n > 420
n > 32.30 or 33 pieces per day
I have to google more problems to work. Only the physics-ish one came naturally.
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