A3 Solve for x: 22x+7 = 8x+1
Since 8=23 let’s rewrite that as 22x+7
= 23(x+1)
So 2x+7 = 3(x+1)
distribute the 3:
2x+7= 3x+3
take 2x from both sides 7=x+3
So x=4
Let’s check our answer. Replace x with 4: 22x+7 =
8x+1
22x4+7
= 84+1
So 215 = 85
Is that true? Without doing all the math let’s express 215
as
(2x2x2)(2x2x2)(2x2x2)(2x2x2)(2x2x2)
Yep, that’s clearly the same as 85
A5 How many integers have a square root between 8/3 and 15/4 ?
Squaring both sides of the sentence, that's really the same as asking
"How many integers are between 64/9 and 225/16?"
or how many integers are between 7.1 and 14.1?
Well, 8, 9, 10, 11, 12, 13, 14. Seven of them.
B3. What value of m makes the equation true?
4 - m = m
4+m m+m+m+m
That's 4 - m = m
4+m 4m
That's 4 - m = 1
4+m 4
Or 4(4 - m) = 4 + m
Thus 16 - 4m = 4 +m
Or 16 = 4 + 5m
Or 12 =5m
Or 12/5 = m
B4. Mr. Olson decided to sell his old washer and dryer. He sold each appliance for $50, which was 25% more than what he expect to get for the washer, and 20% less than what he expected to get for the dryer. In total, how much was Mr. Olson expecting to make for the sale of his appliances?
Let W= what he expected to get for the washer and D= what he expected to get for the dryer.
W+ .25W = 50 D-.20D = 50
1.25W = 50 .80D = 50
W = 40 8D = 500
D=62.50
So what was the question? Oh, he expectd W+D = 40 + 62.50 = $102.50
T4. The price of a stock went up 20% then down 20% before it sold for $48. What was the original price of the stock?
Let P be the original price. So P(1.20)(.80)= $48
Divide both sides by .8 to get P(1.20)= $60
Now divide by (1.20) to get P = $50
Let's check Price $50 up 20% - that's up $10 to $60. Now down 20%. Down 10% would be down $6 so 20% is down 12... it was at 60 so it's $48. Yep.
And finally my favorite impossible problem (drumroll please)
T9. A 5-digit number will be turned into a six digit number by adding a 1 to the beginning of end of the number. If 1 is added to the end the resulting 5-digit number is triple what it would be if the 1 had been added to the beginning. What's the original 5-digit number?
Let n be the 5-digit number. If I add 1 to the end of the number, that's like multiplying by 10 and adding 1. If I add 1 to the beginning that's like adding 100,000. So let's write the equation.
10n + 1 = 3 (100,000 + n)
10n + 1 = 300,000 + 3n
7n + 1 = 300,000
7n = 299,999
n = 42857
I'll let you multiply 3 x 142857 to verify the magical answer.
